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spectrum.py
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spectrum.py
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from scipy.stats import chi2
import numpy as np
def cspectrum(n,m,x,p):
'''Continuous spectrum analysis of an one-dimensional series
Input parameters and arrays: n, m, x, p
n: number of data
m: biggest lag time length. Generally, m is between n/3 and n/10.
x: raw series
p: confidence for red or white noise (e.g. 0.01 for 99%)
Output variables:
ol: frequency array
tl: periodic array
sl: power spectrum. Its sum from 0 to m is 1.
st: (1-p) confidence upper limit of red or white noise spectrum
strw: spectrum density of red or white noise
Usage:
See sanity check in main or just run this script.
The original code is written by Dr. Li Jianping in Fortran77 on May 12, 1998.
http://lijianping.cn/dct/attach/Y2xiOmNsYjpmOjk4Mw== (retrieved on May 5, 2022)
This python version is by CUI Yingzhe, May 5, 2022. Email: [email protected]
'''
sl = np.zeros((m 1))
ol = np.zeros((m 1))
tl = np.zeros((m 1))
r = np.zeros((m 1))
y = x.copy()
r[0] = 1
y -= y.mean()
for i in range(1, m 1):
r[i] = sum(y[1:n-i]*y[i 1:n])/n/y.var()
cc = np.pi*np.arange(1,m 1)/m
for l in range(m 1):
sl[l] = r[0] sum(r[1:]*(1 np.cos(cc))*np.cos(l*cc))
sl[0] /= 2
sl[m] /= 2
sl /= m
ol[1:] = np.pi*np.arange(1,m 1)/m
tl[1:] = 2*m/np.arange(1,m 1)
ol[0] = 0
tl[0] = 100*tl[1]
a = sl.sum()/len(sl)
r2 = r[1]*r[1]
v = (2*n-m/2)/m
iv = np.floor(v)
c = chi2.isf(p, iv) (v-iv)*(chi2.isf(p, iv 1) - chi2.isf(p, iv))
if (r[1] > 0):
r3 = 1 r2-2*r[1]*np.cos(np.arange(m 1)*np.pi/m)
strw = a*(1-r2)/r3
st = strw*c/v
else:
strw = a
st = a*c/v
return ol, tl, sl, st, strw
if __name__=="__main__":
'''Sanity check
'''
omega1 = 2*np.pi/10
omega2 = 2*np.pi/100
t = np.arange(1000)
a = np.cos(omega1*t) np.cos(omega2*t)
n = 1000
m = 300
p = 0.01
ol, tl, sl, st, strw = cspectrum(n,m,a,p)
import matplotlib.pyplot as plt
plt.subplot(2,1,1)
plt.plot(t, a)
plt.title('signal', fontsize = 20)
plt.xlim([0,1000])
plt.subplot(2,1,2)
plt.plot(tl, sl, label = 'spectrum')
plt.plot(tl, st, label = '99% red noise test')
plt.xscale('log')
plt.xlim([1,1000])
plt.legend(fontsize = 20)
plt.show()