find phase noise of a given periodic signal using python in python

You can find the phase noise of a given periodic signal in Python by following these steps:

1. First, you will need to calculate the Fourier transform of the signal using Fast Fourier Transform (FFT).
2. Next, identify the peak frequency component (fundamental frequency) of the signal.
3. Compute the phase spectrum at the fundamental frequency.
4. Calculate the noise power by summing the power in the neighboring frequency bins around the fundamental frequency, excluding the fundamental frequency itself.
5. Finally, calculate the phase noise by taking the ratio of noise power to the power at the fundamental frequency.

Here's an example code snippet to demonstrate how you can find the phase noise of a periodic signal in Python:

main.py
import numpy as np

def calculate_phase_noise(signal, fs):
    fft_result = np.fft.fft(signal)
    freqs = np.fft.fftfreq(len(signal), 1/fs)
    fundamental_freq = freqs[np.argmax(np.abs(fft_result))]
    
    fundamental_power = np.abs(fft_result[np.argmax(np.abs(fft_result))])**2
    noise_power = np.sum(np.abs(fft_result[(np.abs(freqs - fundamental_freq) > 1) & (np.abs(freqs - fundamental_freq) < 10)])**2

    phase_noise = 10 * np.log10(noise_power / fundamental_power)
    
    return phase_noise

# Example usage
fs = 1000  # Sampling frequency in Hz
t = np.arange(0, 1, 1/fs)
signal = np.sin(2*np.pi*10*t) + 0.1 * np.random.randn(len(t))

phase_noise = calculate_phase_noise(signal, fs)
print("Phase noise of the signal: {:.2f} dBc/Hz".format(phase_noise))
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In this code, we calculate the phase noise of a sinusoidal signal with some added noise. You can modify the signal array to your own periodic signal to analyze its phase noise.