Turkish Journal of Electrical Engineering and Computer Sciences
Brain-computer interfaces (BCIs) provide a way to monitor and treat neurological diseases. An imp... more Brain-computer interfaces (BCIs) provide a way to monitor and treat neurological diseases. An important application of BCIs is the monitoring and treatment of epilepsy, a neurological disorder characterized by recurrent unprovoked seizures, symptomatic of abnormal, excessive or synchronous neuronal activity in the brain. BCIs contain an array of sensors that gather and transmit data under the constrains of low-power and minimal data transmission. Asynchronous sigma delta modulators (ASDMs) are considered an alternative to synchronous analog to digital conversion. ASDMs are non-linear feedback systems that enable time-encoding of analog signals, from which the signal can be reconstructed. An efficient reconstruction of time-encoded signals can be achieved using a prolate spheroidal waveform (PSW) projection. PSWs have finite time support and maximum energy concentration within a given bandwidth. The ASDM time-encoding is related to the duty-cycle modulation and demodulation, which shows that sampling is non-uniform. For transmission of data from BCI, we propose a modified orthogonal frequency division multiplexing (OFDM) technique using chirp modulation. Our method generalizes the chirp modulation of binary streams with non-uniform symbol duration. Our theoretical results relate to recent continuous-time digital signal processing and compressive sampling theories.
1995 International Conference on Acoustics, Speech, and Signal Processing
In this paper, we present a connection between the discrete Gabor expansion and the evolutionary ... more In this paper, we present a connection between the discrete Gabor expansion and the evolutionary spectral theory. Including a scale parameter in the Gabor expansion, we obtain a new representation for deterministic signals that is analogous to the Wold-Cramer decomposition for non-stationary processes. The energy distribution resulting from the expansion is easily calculated from the Gabor coe cients. By choosing gaussian windows and appropriate scales, the expansion can represent narrow-band and wide-band signals, as well as their combination. As an application, we consider the masking of signals in the timefrequency space and provide an approximate implementation using the new Gabor expansion. Examples illustrating the time-frequency analysis and the masking are given.
Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing
We propose an adaptive procedure to model non-stationary signals using autoregressive systems wit... more We propose an adaptive procedure to model non-stationary signals using autoregressive systems with time{varying parameters. A non{stationary signal that is representable by a time{varying autoregressive system has parameters which are expandable in terms of a set of basis functions. The parameters can be found by posing a minimum least{squares modeling problem and solving a large set of normal equations. The costly calculations involved in this problem make an adaptive solution quite desirable. Using the parameter expansions, we convert the modeling into a linear prediction problem and solve it adaptively for a given set of basis functions. We apply our procedure in the modeling of a segment of speech and in the estimation of the evolutionary spectrum of a non{stationary signal.
2008 16th European Signal Processing Conference, 2008
In this paper, we show that the Whittaker-Shannon (WS) sampling theory can be modified for the re... more In this paper, we show that the Whittaker-Shannon (WS) sampling theory can be modified for the reconstruction of non-bandlimited signals. According to the uncertainty principle, non-bandlimited signals have finite time support and thus are more common in practical application. Prolate spheroidal wave functions also called Slepian functions have finite time support and maximum energy concentration within a given bandwidth, so instead of infinite length sinc functions, we consider Slepian functions. We show that by projecting non-bandlimited signals onto the space represented by an orthonormal Slepian basis the minimum sampling rate can be reduced nearly by half, with no aliasing. Moreover, the reconstruction error is much lower than the one obtained by the WS theory. In some cases, depending on the desired reconstruction accuracy, it is possible to lower the rate even further. Simulations show the efficiency of the Slepian functions in the reconstruction of uniformly or non-uniformly...
2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221)
In this paper, we propose a new method to estimate instantaneous frequency using a combined appro... more In this paper, we propose a new method to estimate instantaneous frequency using a combined approach based on the discrete linear chirp transform (DLCT) and the Wigner distribution (WD). The DLCT locally represents a signal as a superposition of linear chirps while the WD provides maximum energy concentration along the instantaneous frequency in the time-frequency domain for each of the chirps. The developed approach takes advantage of the separation of the linear chirps given by the DLCT, and that for each of them, the WD provides an ideal representation. Combining the WD of the linear chirp components, we obtain a time-frequency representation free of cross-terms that clearly displays the instantaneous frequency. Applying this procedure locally, we obtain an instantaneous frequency estimate of a non-stationary multicomponent signal. The proposed method is illustrated by simulation. The results indicate the method is efficient for the instantaneous frequency estimation of multicomponent signals embedded in noise, even in cases of low signal to noise ratio.
Proceedings of the IEEE 13th Signal Processing and Communications Applications Conference, 2005.
... Systems Seda Senay 1 , Aydın Akan 2 ve Luis F. Chaparro 3 Elektrik-Elektronik Mühendisli˘gi B... more ... Systems Seda Senay 1 , Aydın Akan 2 ve Luis F. Chaparro 3 Elektrik-Elektronik Mühendisli˘gi Bölümü 1 Yeditepe ¨Universitesi, Kayısda˘gı, ˙Istanbul. ssenay@ yeditepe.edu.tr 2 ˙Istanbul ¨Universitesi, 34320, Avcılar, ˙Istanbul. ...
Acoustics, Speech, and Signal Processing, 1988. ICASSP-88., 1988 International Conference on
In this paper, we present a Gabor representation based on a non-rectangular tiling of the time-fr... more In this paper, we present a Gabor representation based on a non-rectangular tiling of the time-frequency plane and use it to improve the time and frequency resolutions of evolutionary spectra. In the traditional Gabor expansion, a signal is decomposed into a weighted combination of sinusoidally modulated windows resulting in a rectangular time-frequency plane tiling. Poor time and frequency localizations occur in the evolutionary spectrum when the corresponding signal is not modeled well by this xed-window analysis. We are thus proposing the warped Gabor representation based on a linear chirp model for the signal. By means of a frequency transformation we are able to use the previous sinusoidal representation and choose the Gabor coe cients according to either a frequency masking or an energy concentration measure. Examples are given to illustrate our procedures.
In this work, we present a discrete fractional Gabor representation on a general, non-rectangular... more In this work, we present a discrete fractional Gabor representation on a general, non-rectangular timefrequency lattice. The traditional Gabor expansion represents a signal in terms of time and frequency shifted basis functions, called Gabor logons. This constant-bandwidth analysis uses a fixed, and rectangular time-frequency plane tiling. Many of the practical signals require a more flexible, non-rectangular time-frequency lattice for a compact representation. The proposed fractional Gabor method uses a set of basis functions that are related to the fractional Fourier basis and generate a non-rectangular tiling. Simulation results are presented to illustrate the performance of our method.
Multi-carrier spread spectrum (MCSS) communication systems are able to mitigate the effects of fa... more Multi-carrier spread spectrum (MCSS) communication systems are able to mitigate the effects of fading, interferences and Doppler frequency shifts as well as to support multiple access schemes. It is possible to get optimum performance from MCSS systems by carefully choosing the spreading sequences. However, due to inter-user interferences, performance degrades as the number of users increases unless the transmission channels are modeled and estimated. In this paper, we present a new spreading sequence obtained from a complex quadratic sequence multiplied by a pseudo random noise sequence, thus exploiting the properties of constant envelope and statistical independence. Our approach is based on the time-frequency characterization of the wireless communication channel by means of discrete evolutionary transform. The properties of the new spreading sequence enables us to estimate the parameters of multiuser channels, both for uplink and downlink transmission cases, and design a receiver that is robust to channel noise, inter-user interference and intentional jammers. The performance of the proposed system is illustrated by simulations.
2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03).
Power Spectral Density of a signal is calculated from the second order statistics and provides va... more Power Spectral Density of a signal is calculated from the second order statistics and provides valuable information for the characterization of stationary signals. This information is only sufficient for Gaussian and linear processes. Whereas, most real-life signals, such as biomedical, speech, and seismic signals may have non-Gaussian, non-linear and non-stationary properties. Higher Order Statistics (HOS) are useful for the analysis of such signals. Time-Frequency (TF) analysis methods have been developed to analyze the time-varying properties of non-stationary signals. In this work, we combine the HOS and the TF approaches, and present a method for the calculation of a Time-Dependent Bispectrum based on the positive distributed Evolutionary Spectrum.
... SIGNAL PROCESSING ELS EVIER Signal Processing 63 (1997) 249262 Multiwindow Gabor expansion fo... more ... SIGNAL PROCESSING ELS EVIER Signal Processing 63 (1997) 249262 Multiwindow Gabor expansion for evolutionary spectral analysis Aydin Akan'1, Luis F. Chaparro1 ... Als Anwendung prasentieren wir die Berechnung einer Naherung einer ZeitFrequenzDarstellung. ...
Turkish Journal of Electrical Engineering and Computer Sciences
Brain-computer interfaces (BCIs) provide a way to monitor and treat neurological diseases. An imp... more Brain-computer interfaces (BCIs) provide a way to monitor and treat neurological diseases. An important application of BCIs is the monitoring and treatment of epilepsy, a neurological disorder characterized by recurrent unprovoked seizures, symptomatic of abnormal, excessive or synchronous neuronal activity in the brain. BCIs contain an array of sensors that gather and transmit data under the constrains of low-power and minimal data transmission. Asynchronous sigma delta modulators (ASDMs) are considered an alternative to synchronous analog to digital conversion. ASDMs are non-linear feedback systems that enable time-encoding of analog signals, from which the signal can be reconstructed. An efficient reconstruction of time-encoded signals can be achieved using a prolate spheroidal waveform (PSW) projection. PSWs have finite time support and maximum energy concentration within a given bandwidth. The ASDM time-encoding is related to the duty-cycle modulation and demodulation, which shows that sampling is non-uniform. For transmission of data from BCI, we propose a modified orthogonal frequency division multiplexing (OFDM) technique using chirp modulation. Our method generalizes the chirp modulation of binary streams with non-uniform symbol duration. Our theoretical results relate to recent continuous-time digital signal processing and compressive sampling theories.
1995 International Conference on Acoustics, Speech, and Signal Processing
In this paper, we present a connection between the discrete Gabor expansion and the evolutionary ... more In this paper, we present a connection between the discrete Gabor expansion and the evolutionary spectral theory. Including a scale parameter in the Gabor expansion, we obtain a new representation for deterministic signals that is analogous to the Wold-Cramer decomposition for non-stationary processes. The energy distribution resulting from the expansion is easily calculated from the Gabor coe cients. By choosing gaussian windows and appropriate scales, the expansion can represent narrow-band and wide-band signals, as well as their combination. As an application, we consider the masking of signals in the timefrequency space and provide an approximate implementation using the new Gabor expansion. Examples illustrating the time-frequency analysis and the masking are given.
Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing
We propose an adaptive procedure to model non-stationary signals using autoregressive systems wit... more We propose an adaptive procedure to model non-stationary signals using autoregressive systems with time{varying parameters. A non{stationary signal that is representable by a time{varying autoregressive system has parameters which are expandable in terms of a set of basis functions. The parameters can be found by posing a minimum least{squares modeling problem and solving a large set of normal equations. The costly calculations involved in this problem make an adaptive solution quite desirable. Using the parameter expansions, we convert the modeling into a linear prediction problem and solve it adaptively for a given set of basis functions. We apply our procedure in the modeling of a segment of speech and in the estimation of the evolutionary spectrum of a non{stationary signal.
2008 16th European Signal Processing Conference, 2008
In this paper, we show that the Whittaker-Shannon (WS) sampling theory can be modified for the re... more In this paper, we show that the Whittaker-Shannon (WS) sampling theory can be modified for the reconstruction of non-bandlimited signals. According to the uncertainty principle, non-bandlimited signals have finite time support and thus are more common in practical application. Prolate spheroidal wave functions also called Slepian functions have finite time support and maximum energy concentration within a given bandwidth, so instead of infinite length sinc functions, we consider Slepian functions. We show that by projecting non-bandlimited signals onto the space represented by an orthonormal Slepian basis the minimum sampling rate can be reduced nearly by half, with no aliasing. Moreover, the reconstruction error is much lower than the one obtained by the WS theory. In some cases, depending on the desired reconstruction accuracy, it is possible to lower the rate even further. Simulations show the efficiency of the Slepian functions in the reconstruction of uniformly or non-uniformly...
2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221)
In this paper, we propose a new method to estimate instantaneous frequency using a combined appro... more In this paper, we propose a new method to estimate instantaneous frequency using a combined approach based on the discrete linear chirp transform (DLCT) and the Wigner distribution (WD). The DLCT locally represents a signal as a superposition of linear chirps while the WD provides maximum energy concentration along the instantaneous frequency in the time-frequency domain for each of the chirps. The developed approach takes advantage of the separation of the linear chirps given by the DLCT, and that for each of them, the WD provides an ideal representation. Combining the WD of the linear chirp components, we obtain a time-frequency representation free of cross-terms that clearly displays the instantaneous frequency. Applying this procedure locally, we obtain an instantaneous frequency estimate of a non-stationary multicomponent signal. The proposed method is illustrated by simulation. The results indicate the method is efficient for the instantaneous frequency estimation of multicomponent signals embedded in noise, even in cases of low signal to noise ratio.
Proceedings of the IEEE 13th Signal Processing and Communications Applications Conference, 2005.
... Systems Seda Senay 1 , Aydın Akan 2 ve Luis F. Chaparro 3 Elektrik-Elektronik Mühendisli˘gi B... more ... Systems Seda Senay 1 , Aydın Akan 2 ve Luis F. Chaparro 3 Elektrik-Elektronik Mühendisli˘gi Bölümü 1 Yeditepe ¨Universitesi, Kayısda˘gı, ˙Istanbul. ssenay@ yeditepe.edu.tr 2 ˙Istanbul ¨Universitesi, 34320, Avcılar, ˙Istanbul. ...
Acoustics, Speech, and Signal Processing, 1988. ICASSP-88., 1988 International Conference on
In this paper, we present a Gabor representation based on a non-rectangular tiling of the time-fr... more In this paper, we present a Gabor representation based on a non-rectangular tiling of the time-frequency plane and use it to improve the time and frequency resolutions of evolutionary spectra. In the traditional Gabor expansion, a signal is decomposed into a weighted combination of sinusoidally modulated windows resulting in a rectangular time-frequency plane tiling. Poor time and frequency localizations occur in the evolutionary spectrum when the corresponding signal is not modeled well by this xed-window analysis. We are thus proposing the warped Gabor representation based on a linear chirp model for the signal. By means of a frequency transformation we are able to use the previous sinusoidal representation and choose the Gabor coe cients according to either a frequency masking or an energy concentration measure. Examples are given to illustrate our procedures.
In this work, we present a discrete fractional Gabor representation on a general, non-rectangular... more In this work, we present a discrete fractional Gabor representation on a general, non-rectangular timefrequency lattice. The traditional Gabor expansion represents a signal in terms of time and frequency shifted basis functions, called Gabor logons. This constant-bandwidth analysis uses a fixed, and rectangular time-frequency plane tiling. Many of the practical signals require a more flexible, non-rectangular time-frequency lattice for a compact representation. The proposed fractional Gabor method uses a set of basis functions that are related to the fractional Fourier basis and generate a non-rectangular tiling. Simulation results are presented to illustrate the performance of our method.
Multi-carrier spread spectrum (MCSS) communication systems are able to mitigate the effects of fa... more Multi-carrier spread spectrum (MCSS) communication systems are able to mitigate the effects of fading, interferences and Doppler frequency shifts as well as to support multiple access schemes. It is possible to get optimum performance from MCSS systems by carefully choosing the spreading sequences. However, due to inter-user interferences, performance degrades as the number of users increases unless the transmission channels are modeled and estimated. In this paper, we present a new spreading sequence obtained from a complex quadratic sequence multiplied by a pseudo random noise sequence, thus exploiting the properties of constant envelope and statistical independence. Our approach is based on the time-frequency characterization of the wireless communication channel by means of discrete evolutionary transform. The properties of the new spreading sequence enables us to estimate the parameters of multiuser channels, both for uplink and downlink transmission cases, and design a receiver that is robust to channel noise, inter-user interference and intentional jammers. The performance of the proposed system is illustrated by simulations.
2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03).
Power Spectral Density of a signal is calculated from the second order statistics and provides va... more Power Spectral Density of a signal is calculated from the second order statistics and provides valuable information for the characterization of stationary signals. This information is only sufficient for Gaussian and linear processes. Whereas, most real-life signals, such as biomedical, speech, and seismic signals may have non-Gaussian, non-linear and non-stationary properties. Higher Order Statistics (HOS) are useful for the analysis of such signals. Time-Frequency (TF) analysis methods have been developed to analyze the time-varying properties of non-stationary signals. In this work, we combine the HOS and the TF approaches, and present a method for the calculation of a Time-Dependent Bispectrum based on the positive distributed Evolutionary Spectrum.
... SIGNAL PROCESSING ELS EVIER Signal Processing 63 (1997) 249262 Multiwindow Gabor expansion fo... more ... SIGNAL PROCESSING ELS EVIER Signal Processing 63 (1997) 249262 Multiwindow Gabor expansion for evolutionary spectral analysis Aydin Akan'1, Luis F. Chaparro1 ... Als Anwendung prasentieren wir die Berechnung einer Naherung einer ZeitFrequenzDarstellung. ...
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Papers by Luis F. Chaparro