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import numpy as np
from scipy.fft import rfft, rfftfreq
def spectrum(t, y):
"""
Calculate spectrum of real value signal with stripped away zero frequency component.
Preserves amplitude of a coherent signal (Asin(f*t)) independent of sampling
rate and time interval.
"""
N = t.size
dt=np.mean(np.diff(t))
freq=rfftfreq(N, dt)
# y= y - np.mean(y)
yf = rfft(y)
yf *= 2/N; # produce normalized amplitudes
return freq[1:], yf[1:]; # strip of boring freq=0
def noise_density_spectrum(t,y):
"""
Calculate noise amplitude spectral density (ASD), the end results has unitis of y/sqrt(Hz)
i.e. it does sqrt(PSD) where PSD is powerd spectrum density.
Preserves the density independent of sampling rate and time interval.
"""
freq, yf = spectrum(t, y)
yf = yf*np.sqrt(t[-1]-t[0]) # scales with 1/sqrt(RBW)
return freq, yf
def noise_spectrum_smooth(fr, Ampl, Nbins=100):
"""
Smooth amplitude spectrum, especially at high frequency end.
Could be thought as logarithmic spacing running average.
Since we assume the spectrum of the nose, we do power average (rmsq on amplitudes)
Assumes that set of frequencies is positive and equidistant set.
Also assumes that frequencies do not contain 0.
"""
frEdges = np.logspace(np.log10(fr[0]), np.log10(fr[-1]), Nbins)
frCenter = np.zeros(frEdges.size-1)
power = np.zeros(frEdges.size-1)
for i, (frStart, frEnd) in enumerate(zip(frEdges[0:-1], frEdges[1:])):
# print (f"{i=} {frStart=} {frEnd}")
ind = (frStart <= fr) & (fr <= frEnd)
frCenter[i] = np.mean( fr[ind] )
power [i] = np.mean( np.power( np.abs(Ampl[ind]),2) )
ind = np.logical_not(np.isnan(frCenter))
frCenter = frCenter[ind]
power = power[ind]
# print(f'{frCenter=} {power=}')
return frCenter, np.sqrt( power )
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