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DSP_tools.py
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DSP_tools.py
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from scipy.signal import welch
import numpy as np
from detecta import detect_peaks
def get_values(signal,T,N,f_s):
"""Compute the tick values corresponding to the given sampled data y_values.
args:
y_values: sampled values of the signal
T: sampling interval
N: number of samples
f_s: sampling frequency
return:
x_values: tick values of sampled signal
"""
x_values = [T * i for i in range(len(signal))]
return x_values, signal
def get_fft_values(signal,T,N,f_s):
"""Compute FFT of the sampled data besides the corresponding frequency values (0 --> Nyquist frequency)
Nyquist frequency is is the highest possible frequency can be captured from a sampled signal, which
is equal to (f_s/2).
args:
signal: sampled values of the signal
T: sampling interval
N: number of samples
f_s: sampling frequency
return:
f_values: corresponding frequency values
fft_values: amplitude of each sinusoid at each frequency
"""
f_values = np.linspace(0.0,1.0/(2.0*T),N//2)
# we have considered half of the sampled data points due to symmetry nature of FFT
fft_values = np.fft.fft(signal,N) # complex coefficients of fft
fft_values = (2/N) * np.abs(fft_values[:N//2])
return f_values, fft_values
def get_psd_values(signal,T,N,f_s):
"""Computes the power spectral density of the signal using Welch's method, which is an
improvement on the standard periodogram spectrum estimating method.
args:
signal: sampled values of the signal
T: sampling interval
N: number of samples
f_s: sampling frequency
return:
f_values: corresponding frequency values
psd_values: The power distributed over the signal for each frequency.
"""
f_values, psd_values = welch(signal,fs = f_s)
return f_values, psd_values
def autocorr(x):
"""Compute the autocorrelation of discrete signal by means of the convolution
of the signal with its inverse. so the time difference goes from (-N+1,N-1) where N is
the number samples in the signal.
args:
x: the sampled values of the signal
"""
result = np.correlate(x,x,mode = "full")
return result[len(result)//2:] # correlation of the signal in the positive time difference
def get_autocorr_values(signal,T, N, f_s):
""" Compute the autocorrelation of discrete signal and the corresponding time differences
args:
signal: sampled values of the signal
T: sampling interval
N: number of samples
f_s: sampling frequency
return:
dt_values: the time differences values
autocorr_values: the autocorrelation of the discrete signal over the time differences
"""
autocorr_values = autocorr(signal)
dt_values = np.array([T * i for i in range(N)])
return dt_values, autocorr_values