This is a follow up of my previous question Why is inverse CWT inexact / inaccurate?
Rephrasing its accepted answer in my own words:
- The filterbank's transfer function gives information on what band of frequency is well represented using CWT. In my case, an important part of the spectrum lied in the not-so-well-reconstructed region (low frequencies).
- A quick fix for better reconstruction is to remove this part of the spectrum using regular FFT, and the other part can then be accurately reconstructed via CWT.
- The
x_meanargument implements exactly this, only considering the 0 frequency. Your fix is a generalization of this trick
What I mean by generalization is exemplified in the following code (adapted from the answer):
import numpy as np
from numpy.fft import rfft, irfft
import matplotlib.pyplot as plt
from ssqueezepy import cwt, icwt, Wavelet, padsignal
from ssqueezepy.visuals import plot, plotscat
wavelet = Wavelet('gmw')
nv = 16
n = 100
t = np.linspace(0.,1.,n)
x = np.sin(10tt)
n_cutoff = 3
xf = rfft(x)
xf_low = np.copy(xf)
xf_low[n_cutoff:] = 0
xf_high = np.copy(xf)
xf_high[:n_cutoff] = 0
x_high = irfft(xf_high)
x_low = irfft(xf_low)
Wx, scales = cwt(x_high, wavelet=wavelet, nv=nv, padtype=None)
x_high_inv = icwt(Wx, wavelet=wavelet, scales=scales, nv=nv)
x_inv = x_low + x_high_inv
plot(x, color='b')
plot(x_inv, color='r', title="xadj, xadj_inv | MSE=%.3e" % np.mean((x-x_inv)**2))
plt.show()
Setting n_cutoff = 0 is exactly what I strated with (only the mean is being reconstructed), higher values let me treat a larger part of the spectrum independently.
My question is, is my understanding of the referenced answer correct?
