Matplotlib.pyplot.csd() in Python

csd() method in Matplotlib is used to compute and plot the Cross Spectral Density (CSD) of two signals. It helps analyze the frequency domain relationship between two time series, revealing how the power of one signal is distributed relative to the other signal across frequencies. It's key features include:

• Plots the magnitude squared coherence between the signals as a function of frequency.
• Returns the frequency and cross spectral density values for further analysis.
• Useful in signal processing and time series analysis to identify common frequency components.

Example:

import numpy as np
import matplotlib.pyplot as plt

t = np.linspace(0, 1, 500, endpoint=False)
x = np.sin(2 * np.pi * 50 * t) + np.random.randn(t.size) * 0.5
y = np.sin(2 * np.pi * 50 * t) + np.random.randn(t.size) * 0.5

Pxy, freqs = plt.csd(x, y, NFFT=256, Fs=500)
plt.title('Cross Spectral Density')
plt.show()

Output

Explanation:

• np.linspace(0, 1, 500, endpoint=False) creates a 500-point time array at 500 Hz sampling.
• x and y are noisy 50 Hz sine waves simulating real signals.
• plt.csd(x, y, NFFT=256, Fs=500) computes the Cross Spectral Density with 256-point FFT blocks.
• Returns Pxy (CSD) and freqs (frequencies) for frequency analysis.

Syntax of Matplotlib.pyplot.csd()

matplotlib.pyplot.csd(x, y, NFFT=None, Fs=None, detrend=None, window=None, noverlap=None, pad_to=None, scale_by_freq=None, sides='default', hold=None, data=None, **kwargs)

Parameters:

Returns:

• Pxy (ndarray ): The cross spectral density of x and y.
• frequencies (ndarray): The frequencies corresponding to the CSD values.

Examples

Example 1: We compute the cross spectral density of two noisy cosine signals using a Hanning window and 50% overlap between segments to reduce spectral leakage and smooth the result.

import numpy as np
import matplotlib.pyplot as plt
from matplotlib.mlab import window_hanning

t = np.linspace(0, 1, 1000, endpoint=False)
x = np.cos(2 * np.pi * 20 * t) + np.random.randn(t.size) * 0.3
y = np.cos(2 * np.pi * 20 * t) + np.random.randn(t.size) * 0.3

Pxy, freqs = plt.csd(x, y, NFFT=128, Fs=1000, window=window_hanning, noverlap=64)
plt.show()

Output

Explanation:

• np.linspace(0, 1, 1000, endpoint=False) creates a 1000-point time array at 1000 Hz sampling.
• x and y are noisy 20 Hz cosine waves simulating real signals.
• plt.csd(x, y, NFFT=128, Fs=1000, window=window_hanning, noverlap=64) computes the Cross Spectral Density using 128-point FFT blocks with a Hanning window and 64-point overlap to reduce spectral leakage.

Example 2: We compute the cross spectral density of two noisy sine signals using frequency scaling and a one-sided spectrum to highlight how signal power varies with frequency.

t = np.linspace(0, 2, 1000, endpoint=False)
x = np.sin(2 * np.pi * 10 * t) + np.random.randn(t.size) * 0.2
y = np.sin(2 * np.pi * 10 * t) + np.random.randn(t.size) * 0.2

Pxy, freqs = plt.csd(x, y, NFFT=256, Fs=500, scale_by_freq=True, sides='onesided')
plt.title('CSD with Frequency Scaling and One-sided Spectrum')
plt.show()

Output

Explanation:

• np.linspace(0, 2, 1000, endpoint=False) creates a 1000-point time array over 2 seconds.
• x and y are noisy 10 Hz sine waves simulating real signals.
• plt.csd() computes Cross Spectral Density with 256-point FFT blocks, scales by frequency, and returns a one-sided spectrum for clearer frequency analysis.

Example 3: We compute the cross spectral density of two noisy sine signals using detrending to remove DC offset and zero padding to enhance frequency resolution.

t = np.linspace(0, 1, 512, endpoint=False)
x = np.sin(2 * np.pi * 40 * t) + 0.4 * np.random.randn(t.size)
y = np.sin(2 * np.pi * 40 * t) + 0.4 * np.random.randn(t.size)

Pxy, freqs = plt.csd(x, y, NFFT=256, Fs=512, detrend='constant', pad_to=512)
plt.title('CSD with Detrending and Zero Padding')
plt.show()

Output

Explanation:

• np.linspace(0, 1, 512, endpoint=False) creates a 512-point time array at 512 Hz sampling.
• x and y are noisy 40 Hz sine waves simulating real signals.
• plt.csd() computes Cross Spectral Density with 256-point FFT blocks, detrends by removing the mean, and zero-pads to improve frequency resolution.