Abstract: This paper presents an area-time efficient coordinate rotation digital computer (CORDIC) algorithm that completely eliminates the scale-factor. A generalized micro-rotation selection technique based on high speed most-significant-1-detection obviates the complex search algorithms for identifying the micro-rotations. This algorithm is redefined as the elementary angles for reducing the number of CORDIC iterations. Compared to the existing re-cursive architectures the proposed one has 17% lower slice-delay product on Xilinx Spartan XC2S200E device. The CORDIC processor pro-vides the flexibility to manipulate the number of iterations depending on the accuracy, area and latency requirements. Index Terms—coordinate rotation digital computer (CORDIC), cosine/sine, field-programmable gate array(FPGA),most-significant-1, recursive architecture.
VLSI Implementation of CORDIC Based Robot Navigation ProcessorIRJET Journal
This document describes the VLSI implementation of a robot navigation processor based on the CORDIC algorithm and RFID technology. The processor determines the robot's position using signals from RFID tags and avoids collisions by comparing its movement data to that of other robots. It generates a 46-bit data frame containing location, velocity, and direction and uses this information to control the robot's movement. The processor was designed using Verilog HDL, simulated using Xilinx ISE, and its RTL schematic is shown to implement the robot navigation system.
SCS-MCSA- Based Architecture for Montgomery Modular MultiplicationIRJET Journal
The document describes a modified architecture for Montgomery modular multiplication that uses a modified carry save adder (MCSA) to improve performance. The MCSA allows for faster pre-computation and format conversion steps in the Montgomery algorithm compared to using a configurable carry save adder. The proposed SCS-MCSA based Montgomery modular multiplier was implemented on a Xilinx FPGA and achieved lower hardware cost and shorter critical path delay than previous designs. Simulation results showed it requires fewer logic resources and completes a modular multiplication in 8.203 nanoseconds.
The document proposes a new optimized design for a binary coded decimal (BCD) adder using reversible logic gates. It summarizes the basic definitions of reversible logic and describes commonly used reversible gates like CNOT, Toffoli, Peres, TR, and MTSG gates. It then presents the conventional design of a BCD adder and proposes a new design using MTSG gates that has lower quantum cost, fewer gates, and less delay compared to existing designs. The proposed 4-bit reversible BCD adder requires only 10 gates and has a quantum cost of 40.
Andrew Goldberg. Highway Dimension and Provably Efficient Shortest Path Algor...Computer Science Club
The document describes algorithms for computing shortest paths on road networks and proposes a new concept called highway dimension to explain why these algorithms work efficiently. It defines highway dimension and shows how it relates to other graph metrics. The document also analyzes the query time of reach-based and contraction hierarchy algorithms assuming small highway dimension.
This document discusses fast distance matrix computation using contraction hierarchies. It begins with an overview and introduction to distance matrices and their uses in logistics problems. It then discusses standard graph algorithms like Dijkstra's algorithm and bidirectional Dijkstra. Challenges with naive algorithms are presented, including large search spaces. Contraction hierarchies are then introduced as a technique to preprocess the graph to reduce the search space for queries. With contraction hierarchies, the number of explored nodes is reduced dramatically, leading to much faster computation of distance matrices. Results show improvements from hours to seconds for larger problem sizes.
Orthogonal Faster than Nyquist Transmission for SIMO Wireless SystemsT. E. BOGALE
The document proposes a new Orthogonal Faster than Nyquist (OFTN) transmission scheme for SIMO wireless systems that can transmit more than one symbol per time interval, achieving higher spectral efficiency than existing OFDM. The proposed scheme splits the bandwidth into subbands and transmits symbols across subbands and time intervals. It is shown that up to P symbols can be transmitted in 3P-2 time intervals when there are N receive antennas, an improvement over OFDM. Numerical results demonstrate improved bit error rate and sum rate compared to OFDM, especially at high SNR. Open problems remaining include extending the approach to MISO systems and evaluating performance under different channel and system conditions.
DESIGN OF QUATERNARY LOGICAL CIRCUIT USING VOLTAGE AND CURRENT MODE LOGICVLSICS Design
In VLSI technology, designers main concentration were on area required and on performance of the
device. In VLSI design power consumption is one of the major concerns due to continuous increase in chip
density and decline in size of CMOS circuits and frequency at which circuits are operating. By considering
these parameter logical circuits are designed using quaternary voltage mode logic and quaternary current
mode logic. Power consumption required for quaternary voltage mode logic is 51.78 % less as compared
to binary . Area in terms of number of transistor required for quaternary voltage mode logic is 3 times
more as compared to binary. As quaternary voltage mode circuit required large area as compared to
quaternary current mode circuit but power consumption required in quaternary voltage mode circuit is less
than that required in quaternary current mode circuit .
Compiler-driven simulation overcomes issues with gate-level simulation models by compiling a hardware description language (HDL) description of a design directly into an executable simulation model. It differs from event-driven simulation which models the propagation of signals in a circuit over time. The document also asks about the transformation involved in reducing an ordered binary decision diagram (OBDD) into a reduced ordered binary decision diagram (ROBDD) and implementing/constructing an ROBDD. It further inquires about problems investigated in high-level synthesis optimization and describes a simple mobility-based scheduling algorithm with pseudo-code. Finally, it asks about how interval and circular-arc graph coloring performs assignment using a sample of circular arcs and how an input algorithm
This document contains a model examination for a Digital Signal Processing course. It includes two parts - Part A contains 10 short answer questions and Part B contains 5 long answer questions worth 16 marks each. The questions cover various topics in DSP including linear, time-invariant systems, Fourier transforms, FIR and IIR filter design, multirate signal processing, and speech processing applications. Students are required to answer 10 out of 15 questions in total within the 3 hour examination duration.
Acceleration of the Longwave Rapid Radiative Transfer Module using GPGPUMahesh Khadatare
This poster presents Weather Research and Forecast (WRF)
model is a next-generation mesoscale numerical weather
prediction system designed to serve both operational forecasting
and atmospheric research communities. WRF offers multiple
physics options, one of which is the Long-Wave Rapid Radiative
Transfer Model (RRTM). Even with the advent of large-scale
parallelism in weather models, much of the performance increase
has came from increasing processor speed rather than increased
parallelism. We present an alternative method of scaling model
performance by exploiting emerging architectures like GPGPU
using the fine-grain parallelism. We claim to get much more than
23.71x, performance gain by using asynchronous data transfer,
use of texture memory and the techniques like loop unrolling.
This document describes a hardware acceleration approach for N-body simulations using an FPGA. It presents a semi-dataflow architecture and tiling technique to efficiently compute pairwise forces with reduced data transfers. Evaluation shows the FPGA implementation achieves 4400 million particle-pairs per second, outperforming a CPU and achieving high performance per watt compared to other platforms. Future work involves connecting to the host via PCIe and further optimizing performance per watt.
Design and realization of iir digital band stop filter using modified analog ...Subhadeep Chakraborty
This document describes the design and realization of an IIR digital band stop filter using a modified analog to digital mapping technique. It begins with introducing band stop filters and their importance in digital signal processing applications. It then discusses the design of analog band stop filters using passive components like resistors and capacitors. A new algorithm for analog to digital mapping is presented which transforms the transfer function from the s-domain to the z-domain, allowing the analog filter to be realized digitally. The direct form I structure is used to realize the IIR digital band stop filter. Simulation results demonstrating the magnitude response, phase response, impulse response and pole-zero plot are shown for Butterworth band stop filters of orders 6, 8 and 10.
Practical Spherical Harmonics Based PRT MethodsNaughty Dog
The document summarizes methods for compressing precomputed radiance transfer (PRT) coefficients using spherical harmonics. It presents 4 methods with progressively higher compression ratios: Method 1 uses 9 bytes by removing a factor and scaling, Method 2 uses 6 bytes with a bit field allocation, Method 3 uses 6 bytes with a Lloyd-Max non-uniform quantizer, and Method 4 achieves 4 bytes with a different bit allocation. The methods are evaluated based on storage size, reconstruction quality, and rendering performance.
This document discusses digital filters and their implementation in Verilog. It covers:
- Types of digital filters including low-pass, high-pass, band-pass, and band-stop filters
- Finite impulse response (FIR) filters and their implementation using multiplication and addition
- An example 5-tap FIR filter implemented in Verilog
- Infinite impulse response (IIR) filters and their implementation using feedback registers
- An example single tap IIR filter implemented in Verilog with combinational and sequential logic blocks
For the full video of this presentation, please visit:
https://www.embedded-vision.com/platinum-members/xnor/embedded-vision-training/videos/pages/may-2019-embedded-vision-summit-rastegari
For more information about embedded vision, please visit:
http://www.embedded-vision.com
Mohammad Rastegari, Chief Technology Officer at Xnor.ai, presents the "Methods for Creating Efficient Convolutional Neural Networks" tutorial at the May 2019 Embedded Vision Summit.
In the past few years, convolutional neural networks (CNNs) have revolutionized several application domains in AI and computer vision. The biggest challenge with state-of-the-art CNNs is the massive compute demands that prevent these models from being used in many embedded systems and other resource-constrained environments.
In this talk, Rastegari explains and contrasts several recent techniques that enable CNN models with high accuracy to consume very little memory and processor resources. These methods include a variety of algorithmic and optimization approaches to deep learning models. Quantization, sparsification and compact model design are three of the major techniques for efficient CNNs, which are discussed in the context of computer vision applications including detection, recognition and segmentation.
1) A 64-bit domino logic adder was designed using a 180nm CMOS technology for energy and speed optimization.
2) The adder was implemented using 16 slices of a 4-bit carry look-ahead adder connected in a ripple carry fashion.
3) Simulation results showed the 64-bit adder had a latency of 33 clocks and average power consumption of 4.65 microwatts, providing a faster speed compared to a standard 64-bit ripple carry adder.
The document describes optimizing a lighting calculation for the SPU by analyzing memory requirements, partitioning data, and rearranging data for a streaming model. It then provides an example of optimizing a lighting calculation function, including vectorizing the calculation by hand to process 4 vertices simultaneously. The optimizations reduced the calculation time from 231.6 cycles per vertex per light to 208.5 cycles through compiler hints and further to an estimated higher performance by manual vectorization.
LightFields.jl: Fast 3D image reconstruction for VR applications - Hector And...PyData
Virtual Reality plays the leading role on the new media revolution with Light Field reconstruction as a common technique for content generation.High industrial interests make this technique hard to understand and implement, I will present a novel method to reconstruct the depth of objects in images.
The document contains questions that appear to be from an exam on embedded systems design and biomedical signal processing. It includes 10 questions split into two parts (A and B) on these topics. Some of the questions ask students to:
- Describe design metrics that may compete with one another in embedded systems.
- Derive an expression for the percentage revenue loss of a product based on rise angle.
- Determine volumes that yield lowest total cost for different IC technologies.
- Explain concepts like pipelining, digital filters, real-time clocks, and data reduction algorithms.
With entry of time proportion of maturing and incessant infections going high and high. That is the reason people groups are for the most part stressed over their great wellbeing. Furthermore, they are energized by their longing for better wellbeing administration. Individuals intrigues, consideration move towards quiet focused rather than old customary and traditional hospitalized administrations. For this reason in later past thought of U-HEALTHCARE was embraced. U-HealthCare was such a framework made out of a shrewd headband and a wellbeing state screen program. U-Health Care is in charge of keeping under perceptions diverse conditions of wellbeing amid running, strolling, running. Its produce data about heart rate, client PGG (Photo Plet hy Smography) with help of savvy headband. A sticks of time clock proceeds recently investigate on telemedicine drive forward omnipresent social insurance (U-Health).researchers and designers have anticipating such a telemedicine framework which is arrangement of MOBILE, UBIQUITOUS and WIRELESS BODY AREA NETWORK, on the grounds that such a framework have more positive to appreciate next offspring of U-Health. With giving a great deal of productive results present photograph of U-Health framework is still a tiny bit unclear and dark because of inadequacies which make question mark on notice alternative of U-HealthCare System. So for this reason, we should need to take incorporation of most recent, very much modern equipment, correspondences, interconnections, a trademark figuring, advance steering and protection to upcoming offspring of U-Healthcare taking into account MOBILE, UBIQUITOUS and WIRELESS BODY AREA NETWORK. Our distinct fascination and consideration will be on change of ROUTING and SECURITY.
FPGA Implementation of Mixed Radix CORDIC FFTIJSRD
In this Paper, the architecture and FPGA implementation of a Coordinate Rotation Digital Computer (CORDIC) pipeline Fast Fourier Transform (FFT) processor is presented. Fast Fourier Transforms (FFT) is highly efficient algorithm which uses Divide and Conquer approach for speedy calculation of Discrete Fourier transform (DFT) to obtain the frequency spectrum. CORDIC algorithm which is hardware efficient and avoids the use of conventional multiplication and accumulation (MAC) units but evaluates the trigonometric functions by the rotation of a complex vector by means of only add and shift operations. We have developed Fixed point FFT processors using VHDL language for implementation on Field Programmable Gate Array. A Mixed Radix 8 point DIF FFT/IFFT architecture with CORDIC Twiddle factor generation unit with use of pipeline implementation FFT processor has been developed using Xilinx XC3S500E Spartan-3E FPGA and simulated with maximum frequency of 157.359 MHz for 16 bit length 8 point FFT. Results show that the processor uses less number of LUTs and achieves Maximum Frequency.
Spektralanalyse am technologischen Limit: Anwendungen in der Radioastronomie
Wo Prozessoren in ihrer Leistungsfähigkeit nicht mehr ausreichen, wird programmierbare Logik in Form von FPGAs (Field Programmable Gate Arrays) eingesetzt. Hunderte von Rechenoperationen können damit innert Nanosekunden erledigt werden. Diese Technologie eignet sich vorzüglich für die Echtzeit-Spektralanalyse von Signalen.
Typische Anwendungen finden sich in der Radioastronomie oder der Atmosphärenphysik. Typisch sind die enormen Abtastraten von mehreren Giga-Samples pro Sekunde bei Wandler-Auflösungen von ³ 10 Bit, Signal-Bandbreiten von > 1 GHz, aufgelöst in ³ 16'384 Kanälen. Die Leistungsgrenze wird in diesen Bereichen stetig nach oben geschoben.
Mit dem präsentierten Projekt wurde ein neuer Meilenstein punkto Funktionalität und Verarbeitungsgeschwindigkeit gesetzt. So ist das realisierte Spektrometer 1- oder 2-kanalig konfigurierbar, in der 2-kanaligen Version können beispielsweise die Summen- und Differenzspektren gerechnet werden, oder das Kreuzleistungs-Spektrum. Anstelle der "normalen" Fast Fourier Transform (FFT) wurde eine digitale Filterbank implementiert.
Im Vortrag werden aktuelle und künftige Anwendungen im Bereich der Radioastronomie vorgestellt. Es sind Anlagen und Projekte, die weltweit in Betrieb sind oder in Planung stehen. Messresultate zeigen die enorme Leistungsfähigkeit, aber auch die Grenzen der digitalen Spektralanalyse.
Bruno Stuber, Hochschule für Technik FHNW und Christian Monstein, ETH Zürich
1) The document discusses power spectrum estimation methods for digital signal processing.
2) It describes five common non-parametric power spectrum estimation techniques: periodogram method, modified periodogram method, Bartlett's method, Welch's method, and Blackman-Tukey method.
3) Each method has different tradeoffs between frequency resolution, variance, and bias that make some techniques better for certain applications like feature extraction.
A spectrum analyzer measures the amplitude of an input signal versus frequency. There are two main types: swept tuned and FFT-based. A swept tuned spectrum analyzer sweeps across frequencies to display all components, while an FFT analyzer digitizes and converts the signal to the frequency domain. Key components are the RF attenuator, mixer, IF gain, filter, detector, video filter, local oscillator, sweep generator and display. It can operate over a wide frequency range at a lower cost than other analyzers, but cannot measure phase or transient events.
This document discusses spectral analysis in Matlab, including power spectral density, mean-square spectrum, and pseudospectrum estimators. It also covers using the fdatool tool for spectral analysis and designing filters. Finally, it briefly introduces Fourier analysis and decomposing signals into constituent frequencies, and provides a link to additional self-help tutorials on data mining tools.
Analysis of Annual Rainfall Climate Variability in Saudi Arabia by Using Spec...Amro Elfeki
Analysis of Annual Rainfall Climate Variability in Saudi Arabia by Using Spectral Density Function. The 5th International Conference on Water Resources and Arid Environments, January 6-9, 2013.
Area Time Efficient Scaling Free Rotation Mode Cordic Using Circular TrajectoryIOSR Journals
Abstract: This paper presents an area-time efficient Coordinate Rotation Digital Computer (CORDIC) algorithm that completely eliminates the scale-factor. Besides we have proposed an algorithm to reduce the number of CORDIC iterations by increasing the number of stages. The efficient scale factor compensation techniques are proposed which adversely effect the latency/throughput of computation. The proposed CORDIC algorithm provides the flexibility to manipulate the number of iterations depending on the accuracy, area and latency requirements. The CORDIC is an iterative arithmetic algorithm for computing generalized vector rotations without performing multiplications. Index Terms: coordinate rotation digital computer (CORDIC), cosine/sine, field-programmable gate array (FPGA), most-significant-1, recursive architecture, Discrete Fourier Transform (DFT), Discrete Cosine transform (DCT), Iterative CORDIC, Pipelined CORDIC.
Reconfigurable CORDIC Low-Power Implementation of Complex Signal Processing f...Editor IJMTER
This document describes a proposed low-power CORDIC-based DCT architecture that prioritizes processing of low-frequency DCT coefficients over high-frequency coefficients to reduce power consumption with minimal image quality degradation. It uses a look-ahead CORDIC approach to allow varying the number of CORDIC iterations for different coefficients. Experimental results show the proposed architecture achieves 38.1% area and power savings compared to DA-based DCT, with comparable power to MCM-based DCT but using 100% less area and a minor 0.04dB quality loss.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
Designing of cordic processor in verilog using xilinx ise simulatoreSAT Publishing House
This document describes the design of a CORDIC processor in Verilog using Xilinx ISE simulator. CORDIC (COordinate Rotation DIgital Computer) is an iterative algorithm that can calculate trigonometric, hyperbolic and logarithmic functions using only addition, subtraction and shift operations. The designed CORDIC processor takes Cartesian vector inputs (x,y) and an angle theta to calculate the sine and cosine of the input angle. It is implemented using combinatorial logic and operates in rotation mode with 16 iterations for 17-bit inputs and outputs. The design is simulated and tested using a testbench waveform in Xilinx ISE simulator.
Implementation of Rotation and Vectoring-Mode Reconfigurable CORDICijtsrd
CORDIC or CO-ordinate Rotation Digital Computer is a fast, simple, efficient and powerful algorithm used for diverse Digital Signal Processing applications. Primarily developed for real-time airborne computations, it uses a unique computing technique which is especially suitable for solving the trigonometric relationships involved in plane co-ordinate rotation and conversion from rectangular to polar form. It comprises a special serial arithmetic unit having three shift registers, three adders/subtractors, Look-Up table and special interconnections. In this project A CORDIC-based processor for sine/cosine calculation was designed using VHDL programming in Xilinx ISE 13.2. The CORDIC module was tested for its functionality and correctness by test-bench analysis. Subsequently, FPGA implementation of the CORDIC core followed by Chip Scope Pro analysis of the output logic waveforms was performed. Kothapally Mounika | P. Pavan Kumar | K. Shobha Rani"Implementation of Rotation and Vectoring-Mode Reconfigurable CORDIC" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-4 , June 2018, URL: http://www.ijtsrd.com/papers/ijtsrd14396.pdf http://www.ijtsrd.com/engineering/electronics-and-communication-engineering/14396/implementation-of-rotation-and-vectoring-mode-reconfigurable-cordic/kothapally-mounika
Iaetsd finger print recognition by cordic algorithm and pipelined fftIaetsd Iaetsd
This document proposes an efficient CORDIC pipelined FFT algorithm for fingerprint recognition on FPGAs. The CORDIC algorithm uses only shift and add operations, making it suitable for replacing multipliers in the butterfly operations of an FFT. This reduces computational complexity. The proposed system takes a fingerprint, processes it with the CORDIC pipelined FFT, extracts features which are stored and then matched against a test fingerprint for recognition. The algorithm aims to provide an efficient hardware implementation of FFT and fingerprint recognition using minimal computations.
Comparative analysis of multi stage cordic using micro rotation techniqueIAEME Publication
This document presents a comparative analysis of multi-stage CORDIC algorithms using a micro-rotation technique. It proposes a novel pipelined CORDIC architecture for efficient hardware implementation of trigonometric functions. The architecture reduces critical path delay by dividing the CORDIC rotations into multiple pipeline stages. It also suggests a generalized micro-rotation selection technique to reduce the number of iterations needed. Simulation results on a Xilinx FPGA show the proposed design has 51.9% lower slice-delay product and consumes 0.192 watts of power, demonstrating improved efficiency over other CORDIC implementations.
HARDWARE EFFICIENT SCALING FREE VECTORING AND ROTATIONAL CORDIC FOR DSP APPLI...VLSICS Design
1) The document presents a new scaling free CORDIC algorithm for vectoring and rotational modes that requires no pre or post processing. It uses a third order Taylor approximation of sine and cosine functions.
2) The algorithm was implemented on a FPGA using Verilog. Results showed it was fully scaling free, with low power consumption of 0.06mW and delays of 4.123ns and 9.925ns for rotational and vectoring modes respectively.
3) Mathematical verification confirmed the accuracy of 12-16 bits, within expected error bounds for a 16-bit implementation. The proposed algorithm offers improved efficiency over conventional CORDIC.
High speed cordic design for fixed angle of rotationIAEME Publication
This document summarizes a proposed high speed CORDIC design for fixed angle rotation. It begins with an abstract describing the CORDIC algorithm and its applications in digital signal processing, graphics, and other fields. It then discusses prior CORDIC methodologies and their limitations before proposing optimizations to reduce latency and complexity for fixed angle rotation. Specifically, it proposes optimized micro-rotations for fixed angles, single and bi-rotation CORDIC circuits, and carrying out additions using carry select adders to improve speed. The goal is a high speed and less complex CORDIC scheme for fixed angle vector rotation.
Comparative analysis of multi stage cordic using micro rotation techniqIAEME Publication
This document presents a comparative analysis of multi-stage CORDIC algorithms using a micro-rotation technique. It proposes a novel pipelined CORDIC architecture for generating sine and cosine values with improved speed and accuracy. The architecture uses a generalized micro-rotation selection technique to reduce iterations and a high-speed most-significant bit detection scheme to identify micro-rotations without complex search algorithms. Simulation results show the proposed pipelined CORDIC operates at 500MHz with 0.192 watts of power on a Xilinx Vertex4 FPGA, offering 51.9% lower delay and power compared to other approaches.
Comparative analysis of multi stage cordic using micro rotation techniqIAEME Publication
This document presents a comparative analysis of multi-stage CORDIC algorithms using a micro-rotation technique. It proposes a novel pipelined CORDIC architecture for generating sine and cosine values with improved speed and accuracy. The architecture uses a generalized micro-rotation selection technique to reduce iterations and a high-speed most-significant bit detection scheme to identify micro-rotations without complex search algorithms. Simulation results show the proposed pipelined CORDIC operates at 500MHz with 0.192 watts of power on a Xilinx Vertex4 FPGA, offering 51.9% lower delay and power over other approaches.
Comparative analysis of multi stage cordic using micro rotation techniqIAEME Publication
This document summarizes a research paper that proposes a novel pipelined multi-stage CORDIC processor architecture using a micro-rotation selection technique. The CORDIC (coordinate rotation digital computer) algorithm is used to compute trigonometric and other functions through iterative coordinate rotations. The proposed design improves speed by pipelining multiple stages of computation. It also improves efficiency by using a generalized micro-rotation sequence selection based on most-significant bit detection, avoiding complex search algorithms. The architecture reduces computation time and area requirements compared to other CORDIC implementations.
Design and analysis of optimized CORDIC based GMSK system on FPGA platform IJECEIAES
The gaussian minimum shift keying (GMSK) is one of the best suited digital modulation schemes in the global system for mobile communication (GSM) because of its constant envelop and spectral efficiency characteristics. Most of the conventional GMSK approaches failed to balance the digital modulation with efficient usage of spectrum. In this article, the hardware architecture of the optimized CORDIC-based GMSK system is designed, which includes GMSK Modulation with the channel and GMSK Demodulation. The modulation consists of non-return zero (NRZ) encoder, an integrator followed by Gaussian filtering and frequency modulation (FM). The GMSK demodulation consists of FM demodulator, followed by differentiation and NRZ decoder. The FM Modulation and demodulation use the optimized CORDIC model for an In-phase (I) and quadrature (Q) phase generation. The optimized CORDIC is designed by using quadrant mapping and pipelined structure to improve the hardware and computational complexity in GMSK systems. The GMSK system is designed on the Xilinx platform and implemented on Artix-7 and Spartan-3EFPGA. The hardware constraints like area, power, and timing utilization are summarized. The comparison of the optimized CORDIC model with similar CORDIC approaches is tabulated with improvements.
International Journal of Engineering Research and Applications (IJERA) is an open access online peer reviewed international journal that publishes research and review articles in the fields of Computer Science, Neural Networks, Electrical Engineering, Software Engineering, Information Technology, Mechanical Engineering, Chemical Engineering, Plastic Engineering, Food Technology, Textile Engineering, Nano Technology & science, Power Electronics, Electronics & Communication Engineering, Computational mathematics, Image processing, Civil Engineering, Structural Engineering, Environmental Engineering, VLSI Testing & Low Power VLSI Design etc.
A CORDIC based QR Decomposition Technique for MIMO Detection IJECEIAES
CORDIC based improved real and complex QR Decomposition (QRD) for channel pre-processing operations in (Multiple-Input Multiple-Output) MIMO detectors are presented in this paper. The proposed design utilizes pipelining and parallel processing techniques and reduces the latency and hardware complexity of the module respectively. Computational complexity analysis report shows the superiority of our module by 16% compared to literature. The implementation results reveal that the proposed QRD takes shorter lat ency compared to literature. The power consumption of 2x2 real channel matrix and 2x2 complex channel matrix was found to be 12mW and 44mW respectively on the state-of-the-art Xilinx Virtex 5 FPGA.
Reconfigurable Design of Rectangular to Polar Converter using Linear ConvergenceAnuragVijayAgrawal
This document summarizes a research paper that proposes a design for a rectangular to polar converter using a linear convergence algorithm called CORDIC. It discusses how CORDIC iteratively rotates vectors to extract phase and magnitude information in a way that is efficient for FPGAs. The proposed design implements CORDIC in fully parallel form to maximize throughput. It was synthesized and tested on an FPGA, with results showing it can operate at 177.62 MHz with relatively low hardware requirements. Behavioral simulations verified the design matches the expected output.
A verilog based implementation of transcendental function calculator using co...eSAT Journals
Abstract The CORDIC (COordinate Rotation DIgital Computer) algorithm is an iterative algorithm developed by Volder [1] in 1959. It rotates the vector, iteratively and in finite steps to calculate Sine and Cosine of a given angle. Additional work has been done by Walther [2] in 1971. The main principle of CORDIC are calculations based on shift−registers and adders instead of multiplications, which makes use of limited reconfigurable CLB’s in FPGA efficiently saving hardware resources. All trigonometric functions can be computed using vector rotation. CORDIC is also used for polar to rectangular and rectangular to polar conversions, calculation of vector magnitude, and also for transforms like discrete Fourier transform (DFT)/FFT on reconfigurable platform. This paper presents the CORDIC Algorithm for calculation of elementary functions Sine and Cosine in IEEE-754 Format and Q-Format. The paper analyses the feasibility of CORDIC algorithm for implementing the elementary angle computation in FPGA .The CORDIC algorithm is implemented using Verilog language and results are obtained from Xilinx ISE simulation. Keywords: CORDIC, Elementary angle, FPGA, SDR, VHDL
Design and Implementation of Different types of Carry skip adderIRJET Journal
The document describes the design and implementation of different types of carry skip adders. It begins with an introduction to carry skip adders and their advantages over other adder types in terms of speed, area usage, and transistor count. It then reviews existing carry skip adder designs and their limitations. A new design called the Common Boolean Logic (CBL) carry skip adder is proposed that aims to reduce area and power consumption by eliminating redundant adder cells through shared logic. Simulation results show that an 8-bit CBL carry skip adder has 64.6% lower power and 18.7% smaller area than a conventional carry skip adder. In conclusion, the CBL carry skip adder achieves improved performance and efficiency.
IRJET- Implementation of Radix-16 and Binary 64 Division VLSI Realization...IRJET Journal
This document presents four proposed VLSI realization architectures for implementing a high-speed and low-power 64-bit binary division. The architectures use digit-recurrence division algorithms with radix-16 representations and signed digit number systems to represent partial remainders and quotient digits. This allows carry-free addition for calculating next partial remainders and reduces the number of required division iterations. Two representations - static and semidynamic - are used for generating divisor multiples. Radix-16 signed digit sets between [-9,9] are used to represent quotient digits. Carry save and maximally redundant number systems are explored for representing partial remainders to reduce power dissipation. Simulation results show the proposed methods achieve 26-35% lower power
A LIGHT WEIGHT VLSI FRAME WORK FOR HIGHT CIPHER ON FPGAIRJET Journal
This document discusses the implementation of a lightweight VLSI design for the HIGHT cipher on an FPGA. It begins with an introduction to lightweight VLSI architecture and its applications in low-resource devices. It then provides background on the HIGHT cipher and discusses prior work implementing cryptographic algorithms on FPGAs. The document goes on to describe the proposed VLSI design for the HIGHT cipher, which is optimized for size, power, and speed. It achieves a throughput of 25 Mbps with an encryption/decryption delay of 0.64 ms. Evaluation results demonstrate the effectiveness and suitability of the design for low-power applications.
Similar to Implementation of Efficiency CORDIC Algorithmfor Sine & Cosine Generation (20)
This document provides a technical review of secure banking using RSA and AES encryption methodologies. It discusses how RSA and AES are commonly used encryption standards for secure data transmission between ATMs and bank servers. The document first provides background on ATM security measures and risks of attacks. It then reviews related work analyzing encryption techniques. The document proposes using a one-time password in addition to a PIN for ATM authentication. It concludes that implementing encryption standards like RSA and AES can make transactions more secure and build trust in online banking.
This document analyzes the performance of various modulation schemes for achieving energy efficient communication over fading channels in wireless sensor networks. It finds that for long transmission distances, low-order modulations like BPSK are optimal due to their lower SNR requirements. However, as transmission distance decreases, higher-order modulations like 16-QAM and 64-QAM become more optimal since they can transmit more bits per symbol, outweighing their higher SNR needs. Simulations show lifetime extensions up to 550% are possible in short-range networks by using higher-order modulations instead of just BPSK. The optimal modulation depends on transmission distance and balancing the energy used by electronic components versus power amplifiers.
This document provides a review of mobility management techniques in vehicular ad hoc networks (VANETs). It discusses three modes of communication in VANETs: vehicle-to-infrastructure (V2I), vehicle-to-vehicle (V2V), and hybrid vehicle (HV) communication. For each communication mode, different mobility management schemes are required due to their unique characteristics. The document also discusses mobility management challenges in VANETs and outlines some open research issues in improving mobility management for seamless communication in these dynamic networks.
This document provides a review of different techniques for segmenting brain MRI images to detect tumors. It compares the K-means and Fuzzy C-means clustering algorithms. K-means is an exclusive clustering algorithm that groups data points into distinct clusters, while Fuzzy C-means is an overlapping clustering algorithm that allows data points to belong to multiple clusters. The document finds that Fuzzy C-means requires more time for brain tumor detection compared to other methods like hierarchical clustering or K-means. It also reviews related work applying these clustering algorithms to segment brain MRI images.
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Best Practices for Password Rotation and Tools to Streamline the Process
Implementation of Efficiency CORDIC Algorithmfor Sine & Cosine Generation
1. IOSR Journal of Electronics and Communication Engineering (IOSR-JECE)
e-ISSN: 2278-2834,p- ISSN: 2278-8735. Volume 6, Issue 5 (Jul. - Aug. 2013), PP 49-56
www.iosrjournals.org
www.iosrjournals.org 49 | Page
Implementation of Efficiency CORDIC Algorithmfor Sine &
Cosine Generation
P.Keerthi, ShaikJaffar
(M.Tech),Vlsi Design Dept Of Electronics And Communications Madina Engineering College Kadapa, Andhra
Pradesh.
M.Tech, (Ph.D.) Miste, Mie, Assoc.ProfessorDeptOf Electronics And Communications Madina Engineering
College Kadapa, Andhra Pradesh
Abstract: This paper presents an area-time efficient coordinate rotation digital computer (CORDIC) algorithm
that completely eliminates the scale-factor. A generalized micro-rotation selection technique based on high
speed most-significant-1-detection obviates the complex search algorithms for identifying the micro-rotations.
This algorithm is redefined as the elementary angles for reducing the number of CORDIC iterations. Compared
to the existing re-cursive architectures the proposed one has 17% lower slice-delay product on Xilinx Spartan
XC2S200E device. The CORDIC processor pro-vides the flexibility to manipulate the number of iterations
depending on the accuracy, area and latency requirements.
Index Terms—coordinate rotation digital computer (CORDIC), cosine/sine, field-programmable gate
array(FPGA),most-significant-1, recursive architecture.
I. Introduction
For systems such as Calculator, keeping the size of calculator very small is of prime importance. For
these systems the cost (e.g. chip gate count has to be minimized) is more important than speed. Also it is very
important to calculate the values with good accuracy and precision. Though sometimes by increasing the bit
length we can obtain better precision, but it is more important to select a method which gives more accurate
results.
The coordinate rotation digital computer (CORDIC) has established its popularity in several
important areas of application, like generation of sine and cosine functions, calculation of discrete sinusoidal
transforms like fast Fourier transform (FFT), discrete sine/cosine transforms (DST/DCT), householder
transform (HT),etc. [1]–[3]. Manyvariations have been suggested for efficient implementation of CORDIC with
less number of iterations over the conventional CORDIC algorithm.The number of CORDIC iterations are
optimized in [4]–[6] by greedy search at the cost of additional areaand time for the implementation of variable
scale-factor. In efficient scale-factor compensationtechniques are proposed, which adversely affect the
latency/throughput of computation.
Two area-time efficient CORDIC architectures have been suggested , which involve constant scale-
factor multiplication for adequate range of convergence (RoC). The virtually scale-
free CORDIC also requires multiplication by constant scale-factor and relatively more area to achieve
respectable RoC. The enhanced scale-free CORDIC combines few conventional CORDIC iterations with
scaling-free CORDIC iterations for an efficient pipelined CORDIC implementation with improved RoC.
However, if used for recursive CORDIC architecture, combining two different types of CORDIC iterations,
degrades performance. In this paper, we propose a novel scaling-free CORDIC algorithm for area-time efficient
implementation of CORDIC with adequate RoC.
II. Brief Overview Of Cordicalgorithm
CORDIC (Coordinate Rotation Digital Computer) was introduced in 1959 by Jack E. Volder. It is very
efficient to compute the values of sin, cos, sin, tan, sinh, Cosh, tanh. It’s a Hardware Efficient Algorithm. It is
an iterative Algorithm for Circular Rotation. It requires no Multiplication. Delay/Hardware cost comparable to
division or square rooting. Compared to other approaches, CORDIC is a clear winner when:Hardware
Multiplier is unavailable (e.g. microcontroller),You wants to save the gates required to implement (e.g.
FPGA).Its basic ideas is-Embedding of elementary function evaluation as a generalized rotation operation,
Decompose rotation operation into successive basic rotations,Each basic rotation can be realized with shift and
add arithmetic operations. Shift and-add arithmetic operations. To evaluate trigonometric functions we have
many approaches suchas -1) Table lookup2) Polynomial Approximations3)CORDIC.
2. Implementation of Efficiency CORDIC Algorithm For Sine & Cosine Generation
www.iosrjournals.org 50 | Page
A. Taylor Series
The Taylor series expansion for sine is:
sin 𝑥 = 𝑥 −
𝑥3
3!
+
𝑥5
5!
−
𝑥7
7!
+ ⋯
This method is one of the oldest and most widely, but the problem associated with this method is, to get values
of higher accuracies, higher order factorial and power has to be calculated. Moreover to implement this we
would at least require a multiplier, divider, adder and a subtractor. For good accuracy it would be required to
take each term incalculation till they become insignificant. Thus this approach has a lot of hardware
requirements as well as it is slow.
B. Look up Table
The Lookup table approach involves storing values of sine and cosine at different angles. Based on
the number of values stored, the lookup table can be big or small, but clearly, the smaller the lookup table, more
is the error involved. The problem with a bigger lookup table is that it requires more memory and memory is
expensive. Moreover the size of the Lookup table increases exponentially with the increase in the precision of
the angle. Though this approach provides fast results it is very expensive to implement.
C. Cordic Algorithm
CORDIC is an acronym for Coordinate Rotation Digital Computer introduced by Jack E. Volder. It
is an iterative algorithm capable of calculating trigonometric and various other functions. In this algorithm with
the help of an adder/subtractor, a small look up table and a shifter the trigonometric functions can be calculated
very easily. The advantage that Cordic offers over other algorithms are that it does not require multiplication or
division blocks, instead it works only with a shifter, adder/subtractor and a small lookup table. This reduces the
hardware requirement drastically and provides reasonably good speed.
Many variations have been suggested for efficient implementation of CORDIC with less number of
iterations over the conventional CORDIC algorithm [4]–[11]. The number of CORDIC iterations are optimized
in [4]–[6] by greedy search at the cost of additional area and time for the implementation of variable scale-
factor. In [7] and [8] efficient scale-factor compensation techniques are proposed, which adversely affect the
latency/throughput of computation. Two area-time efficient CORDIC architectures have been suggested in [9],
which involve constant scale-factor multiplication for adequate range of convergence (RoC). The virtually
scale-free CORDIC in [10] also requires multiplication by constant scale-factor and relatively more area to
achieve respectable RoC. The enhanced scale-free CORDIC in [11] combines few conventional CORDIC
iterations with scaling-free CORDIC iterations for an efficient pipelined CORDIC implementation with
improved RoC. However, if used for recursive CORDIC architecture, combining two different types of
CORDIC iterations, degrades performance.
The low complexity technique for eliminating the scale factor is the use of Taylor series expansion. The
Scaling-Free CORDIC and modified scale-free CORDIC are techniques based on Taylor series approach. The
former suffers from low range of convergence (RoC) which renders it unsuitable for practical applications,
while the latter extends the RoC but introduces predictable but constant scale-factor of 1/ 2. The other
hardware efficient architectures require scale-factor compensations to extend the range of convergence to the
entire coordinate space.
III. Sequential/Iterative Cordic
It requires Maximum number of Clock Cycles to calculate output,Minimum Clock Period
periteration,Variable Shifters do not map well on certain FPGA’s due to high Fan-in.
3. Implementation of Efficiency CORDIC Algorithm For Sine & Cosine Generation
www.iosrjournals.org 51 | Page
Fig:1.Variable Shifters
Parallel/Cascaded CORDIC:
It hasCombinational circuit More Delay, but processing time is reduced as compared to iterative
circuit.Shifters are of fixed shift, so they can be implemented in the wiring.Constants can be hardwired instead
of requiring storage space.
Fig.2. Parallel/Cascaded CORDIC
Coordinate Rotation Digital Computer is abbreviated as CORDIC. The key concept of CORDIC arithmetic is
based on the simple and ancient principles of two-dimensional geometry. But the iterative formulation of a
computational algorithm for its implementation was first described in 1959 by Jack E. Volder for the
computation of trigonometric functions, multiplication and division. This year therefore marks the completion
of 50 years of the CORDIC algorithm. Not only a wide variety of applications of CORDIC have emerged in the
last 50 years, but also a lot of progress has been made in the area of algorithm design and development of
architectures for high performance and low-cost hardware solutions of those applications. CORDIC-based
computing received increased attention in 1971, by varying a few simple parameters; it could be used as a
single algorithm for unified implementation of a wide range of elementary transcendental functionsinvolving
logarithms, exponentials, and square roots along with those suggested by Volder. During the same time,
Cochran benchmarked various algorithms, and showed that CORDIC technique is a better choice for scientific
calculator applications. The popularity of CORDIC was very much enhanced thereafter primarily due to
itspotential for efficient and low-cost implementation of a large class of applications which include: the
generationof trigonometric, logarithmicand transcendental elementary functions; complex number
multiplication, eigenvalue computation, matrix inversion, solution of linear systems and singular value
decomposition (SVD) for signal processing, image processing, and general scientific computation.
The name CORDIC stands for Coordinate Rotation Digital Computer. Volder [Vold59] developed the
underlying method of computing the rotation of a vector in a Cartesian coordinate system and evaluating the
length and angle of a vector. The CORDIC method was later expanded for multiplication, division, logarithm,
exponential and hyperbolic functions.
4. Implementation of Efficiency CORDIC Algorithm For Sine & Cosine Generation
www.iosrjournals.org 52 | Page
IV. Pipelined Architecture
The principle of pipelining has emerged as a major architectural attribute of most present computer
systems.Pipelining is one form of imbedding parallelism or concurrency in a computer system. It refers to a
segmentation of a computational process (say, an instruction) into several sub processes which are executed by
dedicated autonomous units (facilities, pipelining segments)
Fig.3.Pipe line architecture logical view
Parallel CORDIC can be pipelined by inserting registers between the adders stages. In most FPGA
architectures there are already registers present in each logic cell, so pipeline registers has no hardware cost.
Number of stages after which pipeline register is inserted can be modeled, considering clock frequency of
system.When operating at greater clock period power consumption in later stages reduces due to lesser
switching activity in each clock period.
V. Proposed Algorithm For Scaling Free Cordic :
The proposed design is based on the following key ideas: 1) we use Taylor series expansion of sine
and cosine functions to avoid scaling operation and 2) suggest a generalized sequence of micro-rotation to have
adequate range of convergence (RoC) based on the chosen order of approximation of the Taylor series.
A.Taylor Series Approximation of Sine and Cosine Functions
The Taylor expansions of sine and cosine of an angle “-” are given by
sin ∝= ∝ − 3! −1
∝3
+ 5! −1
∝5
− ⋯
cos ∝ = 1 − 2! −1
∝2
+ 4! −1
∝4
− ⋯
We have estimated the maximum error in the evaluation of sine and cosine functions for different order of
approximations. Therefore, we choose third order of approximation for Taylor’s expansion of sine and cosine
functions.
1) Representation of Micro-Rotations Using Taylor Series Approximation:
Here, we study the impact of orders of approximation ofTaylor series of sine and cosine functions on the
micro-rotations to beused in CORDIC coordinate calculation. Both theoretical and simulationresults are
discussed to confirm the appropriate selection of theorder of approximation. Using different orders of
approximation of sineand cosine functions in (2), we can have
𝑥𝑖+1 = 1 −
∝2
𝑖
2!
. 𝑥𝑖 − ∝𝑖−
∝3
𝑖
3!
. 𝑦𝑖
𝑦𝑖+1 = 1 −
∝2
𝑖
2!
. 𝑦𝑖 + ∝𝑖−
∝3
𝑖
3!
. 𝑥𝑖 (1a)
𝑥𝑖+1 = 1 −
∝2
𝑖
2!
+
∝4
𝑖
4!
. 𝑥𝑖 − ∝𝑖−
∝3
𝑖
3!
. 𝑦𝑖
𝑦𝑖+1 = 1 −
∝2
𝑖
2!
+
∝4
𝑖
4!
. 𝑦𝑖 + ∝𝑖−
∝3
𝑖
3!
. 𝑥𝑖(1b)
𝑥𝑖+1 = 1 −
∝2
𝑖
2!
+
∝4
𝑖
4!
. 𝑥𝑖 − ∝𝑖−
∝3
𝑖
3!
+
∝5
𝑖
5!
. 𝑦𝑖
5. Implementation of Efficiency CORDIC Algorithm For Sine & Cosine Generation
www.iosrjournals.org 53 | Page
𝑦𝑖+1 = 1 −
∝2
𝑖
2!
+
∝4
𝑖
4!
. 𝑦𝑖 + ∝𝑖−
∝3
𝑖
3!
+
∝5
𝑖
5!
. 𝑥𝑖 (1c)𝑥𝑖+1 = 1 −
∝2
𝑖
2!
+
∝4
𝑖
4!
−
∝6
𝑖
6!
. 𝑥𝑖 − ∝𝑖−
∝3
𝑖
3!
+
∝5𝑖5!.𝑦𝑖
𝑦𝑖+1 = 1 −
∝2
𝑖
2!
+
∝4
𝑖
4!
−
∝6
𝑖
6!
. 𝑦𝑖 + ∝𝑖−
∝3
𝑖
3!
+
∝5
𝑖
5!
. 𝑥𝑖(1d)
𝑥𝑖+1 = 1 −
∝2
𝑖
2!
+
∝4
𝑖
4!
−
∝6
𝑖
6!
. 𝑥𝑖 − ∝𝑖−
∝3
𝑖
3!
+
∝5
𝑖
5!
−
∝7
𝑖
7!
. 𝑦𝑖
𝑦𝑖+1 = 1 −
∝2
𝑖
2!
+
∝4
𝑖
4!
−
∝6
𝑖
6!
. 𝑦𝑖 + ∝𝑖−
∝3
𝑖
3!
+
∝5
𝑖
5!
−
∝7
𝑖
7!
. 𝑥𝑖 (1e)
We have used (1) for coordinate calculation for evaluating the best possible combination of approximation,
which satisfies the accuracy and RoC requirements, with minimum possible hardware. In Fig. 1,we have plotted
the error in magnitude estimated according to (1) (with respect to the corresponding built-in functions of
MATLAB). Since Errors resulting from the five combinations (1a)–(1e) are of very small order, we prefer to
use (1a) for coordinate calculation with minimum complexity.
2) Expressions for Micro-Rotations Using Taylor Series Approximation and Factorial Approximation:
Although, we find that we canuse Taylor series expansion with third order of approximation
(1a),with desired accuracy and RoC requirement, (1a)cannot be used inthe CORDIC shift-add iterations. To
implement (1a) by shift-add operations,we need to approximate the factorial terms by the power of 2values,
replacing 3! by 2^3 in the (1a) we find
𝑥𝑖+1
𝑦𝑖+1
=
1 − 2! −1
. ∝𝑖
2
−(∝𝑖− 2−3
∝𝑖
3
)
(∝𝑖− 2−3
∝𝑖
3
) (1 − 2! −1
. ∝𝑖
2
)
.
𝑥𝑖
𝑦𝑖
(2)
In Fig. 1 only, we have plotted the error in magnitude using the approximated factorial values and exact
factorial values after a CORDIC rotation for initial vector with coordinates X=1 and Y=1. The maximum
percentage of error in sine and cosine values for both third order of approximation and factorial approximation
is 0.0004% and 0.0168%, respectively, within the permissible CORDIC elementary angles range of 0,
7𝜋
88
discussed.
B. Determination of the Basic-Shift for a Given Order of Approximation of Taylor Series Expansion
One can find that: 1) the order of approximation of Taylor series expansion of sine and cosine
functions determines the basic-shift to be used for CORDIC iterations, and 2) the basic-shift of CORDIC
microoperation determines the range of convergence. The expressions for the basic-shifts, the first elementary
angle of rotation ∝1 and RoCfor different orders of approximations for different word-length of
implementations are as follows:
Basic shift S=
𝑏−log 2 𝑛+1 !
(𝑛+1)
(3a)
Where b is the wordlength
ROC=𝑛1. ∝1 (3b)
N is number of micro rotations
∝1= 2−𝑠
(3c)
The values in Table I are derived from (3). We find with increase in the order of approximation, the
basic-shift decreases, the first elementary angle of rotation increases and RoC is expanded. Very often inclusion
of higher order terms does not have any impact on the accuracy for smaller word-lengths. The basic-shift for
third order of approximation using (3a), for 16-bit word-length is [2.854].
TABLE I
COMPARISION OF APPROXIMATION ORDERS VERSUS ROC FOR VARIOUS BIT WIDTHS BASED
ON(7)
Order of
Approx.
Basic shift First Elementary Angle
(Radians)
RoC for 𝑛1=4
(Radians)
16-bit 32-bit 16-bit 32-bit 16-bit 32-bit
3 2 6 0.25 0.01562 1 0.0625
4 1 5 0.5 0.03125 2 0.125
5 1 3 0.5 0.125 2 0.5
6. Implementation of Efficiency CORDIC Algorithm For Sine & Cosine Generation
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TABLE II
BIT REPRESENTATION OF ELEMENTARY ANGLES AND CORRESPONDING SHIFTS
Shift
(si)
Elementary angle(𝛼𝑖)
Decimal 16-bit HexaDecimal
2 0.25 4000
3 0.125 2000
4 0.0625 1000
5 0.03125 0800
In this paper, we propose a novel scaling-free CORDIC algorithm for area-time efficient implementation of
CORDIC with adequate RoC. The proposed recursive architecture has comparable or less area complexity with
other existing scaling-free CORDIC algorithms. Moreover, no scale-factor multiplications are required for
extending the RoC to entire coordinate Space.
TABLE III
PSEUDO CODE FOR GENERATING THE MICRO-ROTATION SEQUENCE
Input: angle to be rotated 𝜃𝑖
Begin
M=Most significant-1location(𝜃𝑖)
If(M==15)then
α=0.25 radians
shift,𝑠𝑖 = 2 𝑎𝑛𝑑𝜃𝑖+1 = 𝜃𝑖 − 𝛼
else
shift,𝑠𝑖=16-M
𝜃𝑖+1 = 𝜃𝑖with𝜃𝑖[M]=’0’
END
VI. Proposed Cordic Architecture
The block diagram for the proposed CORDIC architecture is shown in Fig. below. It makes use of
the same stage for all the iterations for the coordinate calculations, as well as for the generation of shift values.
The structure of each stage (shown in Fig. 5) consists of three computing blocks namely the 1) shift-value
estimation; 2) coordinate calculation;and 3) micro-rotation sequence generator.
Fig.4. Recursive architecture of the proposed CORDIC processor.
Fig. 5. Block diagram for the stage.
The combinatorial circuit for generating the micro-rotation sequence is shown in Fig. 4. The number of
iterations required in a CORDIC processor decides the rollover count of the counter. The rollover count is seven
for basic shift =2 and ten for basic-shift =3.
7. Implementation of Efficiency CORDIC Algorithm For Sine & Cosine Generation
www.iosrjournals.org 55 | Page
Fig. 6.Combinatorial circuit for generating the shift values.
The expiry of the counter signals the completion of a CORDIC operation; depending on this signal, the
multiplexer either loads a new data-set (rotation angle,initial value of and “x”and”y”) to start a fresh CORDIC
operation, or recycles the output of the stage to begin a new iteration for the current CORDIC operation. The
input and output register files act as latches for synchronization.
Fig. 7.Micro-rotation sequence generation.
VI. Fpga Implementation
The proposed architecture is coded in Verilog and synthesized using Xilinx ISE9.2i to be
implemented in Xilinx Spartan 2E (XC2S200EPQ208- 6) device. Slice-delay-product of the proposed
architecture is compared with the existing CORDIC designs in Table IV; where, all designs are synthesized on
Xilinx Spartan 2E XC2S200E device to maintain uniformity. The power dissipation of the proposed
architecture for different clock frequencies is estimated by Xilinx XPower tool.
VII. Experimental Result And Discussion
TABLE IV
SLICE DELAY PRODUCT
Slice-delay-product of the proposed architecture is compared with the existing CORDIC designs in
TableIVis suggested to reduce the number of iterations for low latency implementation. The proposed CORDIC
processor has 17% lower slice-delay product for identifying the micro-rotations.
VIII. Conclusion
The proposed algorithm provides a scale-free solution for realizing vector-rotations using CORDIC.
The order of Taylor series approximation is decided appropriately by the proposed algorithm, not only to meet
the accuracy requirement but also to attain adequate range of convergence. The generalized micro-rotation
selection technique is suggested to reduce the number of iterations for low latency implementation. Moreover, a
high speed most-significant-1 detection scheme obviates the complex search algorithms for identifying the
micro-rotations. The proposed CORDIC processor has 17% lower slice-delay product with a penalty of about
13% increased slice consumption on Xilinx Spartan 2E device.
Logic Utilization Used Available Utilizatio
n
Number of Slices 958 5472 17%
Number of Slice Flip Flops 862 10944 7%
Number of 4 input LUTs 1749 10944 15%
Number of bonded IOBs 57 240 23%
Number of GCLKs 1 32 3%
8. Implementation of Efficiency CORDIC Algorithm For Sine & Cosine Generation
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BIOGRAPHIES
P.Keerthi, received B.Tech degree in Electronics & Communication Engineering from
Madanapalle Institute of Technology and Science, Madanapalle,in 2011.Worked as
Assistant Professor in MITS for 6 months. She is now M.Tech scholarin VLSI
Design,Madina Engineering College,Kadapa,AP.
Shaik.Jaffar receivedB.Techdegree in Electronics & Communication Engineering in
1991,M.TechElectronics & Communication Engineering in 2002.He is currently doing
research in JNTUA University.He is having an experience of15years,in the field of
teaching, presently workingas Assco. Professor in the department of ECE, MadinaEngg
College,Kadapa. He is a life time memberof MIE&MISTE.