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Spectral_density.py
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Spectral_density.py
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import numpy as np
import matplotlib.pyplot as plt
from scipy import signal
def sort_x_f(x_unsort,f_unsort):
#x is the varible and f is function
arr_unsort=[x_unsort,f_unsort]
f_x_unsort=tuple(map(tuple, np.transpose(arr_unsort)))
f_x_sort=sorted(f_x_unsort, key=lambda f_x_unsort: f_x_unsort[0])
f_x_sort=np.array(f_x_sort)
f_x_sort=np.transpose(f_x_sort)
x_sort=f_x_sort[0,:]
f_sort=f_x_sort[1,:]
return x_sort,f_sort
#https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.periodogram.html
#'boxcar' Also known as a rectangular window or Dirichlet window, this is equivalent to no window at all.
#window types: https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.get_window.html#scipy.signal.get_window
def spectral_density(function,time,window_for_FFT='boxcar',plot=False):
time=np.array(time)
dt=time[1:]-time[:-1]
dt_min=np.min(dt)
if abs(np.std(dt))>=np.min(dt)*0.01:
print('time step is NOT uniform. interperlating')
uni_time = np.linspace(min(time),max(time),int(abs((max(time)-min(time))/dt_min)*1.5)) #uniform time
uni_function = np.interp(uni_time,time,function)
else:
uni_time=time
uni_function=function
fs=1./np.mean(abs(uni_time[1:]-uni_time[:-1]))
print('avg_dt='+str(np.mean(abs(uni_time[1:]-uni_time[:-1]))))
print('std_dt='+str(np.std(abs(uni_time[1:]-uni_time[:-1]))))
f, Pxx_den = signal.welch(uni_function, fs, window=window_for_FFT) #, scaling='spectrum')
#Sort frequency to monotonic increase
f, Pxx_den=sort_x_f(f, Pxx_den)
if plot==True:
plt.plot(f, Pxx_den,label='Pxx_den')
plt.plot(f, np.sqrt(Pxx_den),label='sqrt(Pxx_den)')
#plt.semilogy(f, Pxx_den)
#plt.ylim([1e-7, 1e2])
plt.xlabel('frequency [Hz]')
plt.ylabel('PSD [V**2/Hz]')
plt.legend()
plt.show()
return f, Pxx_den
'''
#*********Demo function****************
window_input='hann'
timestep0=0.002
time1 = np.arange(0.,2.,timestep0)
time2 = np.arange(2.00001,3.,timestep0*0.1)
#time = time1
time = np.append(time1, time2)
print(str(time))
#time.append(2.001)
#time.extend(time)
frequency=20.
omega = 2.*np.pi*frequency
#function=1+np.exp(-1.j * omega * time -3.j)+0.5*np.exp(+1.j * 2*omega * time-1.j)+0.5*np.exp(+1.j * 3.*omega * time-1.j)
function=np.exp(-1.j * omega * time )+0.5*np.exp(+1.j * 2*omega * time)+2.*np.exp(+1.j * 3.*omega * time)
f, Pxx_den=spectral_density(function,time,window_input,plot=True)
Sum_over_t=np.mean(abs(function)**2.)**0.5
Sum_over_f=(np.sum(Pxx_den)*np.mean(abs(f[:-1]-f[1:])))**0.5
print('f='+str(f))
print('Pxx_den='+str(Pxx_den))
print('np.sum(Pxx_den)='+str(np.sum(Pxx_den)))
print('np.mean(abs(f[:-1]-f[1:]))='+str(np.mean(abs(f[:-1]-f[1:]))))
print('Sum_over_t='+str(Sum_over_t))
print('Sum_over_f='+str(Sum_over_f))
#*********Demo function****************
'''