Why does the fft of the component corresponding to the last approximation coefficient obtained after wavelet decomposition not match the fft of the original signal in the low-frequency region, resulting in an unsmooth frequency response between the two and varying with the original signal. Is using FFT to solve frequency response unreliable?
clearvars;close all;clc;
fs=10;
dt=1/fs;
t=dt:dt:200;
N=length(t);
signal=(0.2)*randn(1,N);
Max_level=wmaxlev(length(signal),’db10′);
[C,L]=wavedec(signal,Max_level,’fk8′);
level=6;
xL_DWT = wrcoef(‘a’,C,L,’fk8′,level);
xH_DWT=signal-xL_DWT;
%fft
Nfft=length(t);
f_DWT = (1:Nfft/2)*fs/(Nfft);
xL_DWT_fft=fftshift(fft(xL_DWT,Nfft));
xH_DWT_fft=fftshift(fft(xH_DWT,Nfft));
signal_fft=fftshift(fft(signal,Nfft));
wn_low_DWT=xL_DWT_fft./signal_fft;
wn_high_DWT=1-wn_low_DWT;
figure
plot(f_DWT,wn_low_DWT(Nfft/2+1:end));
hold on
plot(f_DWT,wn_high_DWT(Nfft/2+1:end));
ylim([-0.5 2]);
yticks([-0.5:0.5:2])
xlim([0 fs/2^(level-1)]);
xticks([0 fs/2^(level+1) fs/2^(level) fs/2^(level-1)])
xticklabels({‘0′,’fs/2^{i+1}’,’fs/2^{i}’,’fs/2^{i-1}’})Why does the fft of the component corresponding to the last approximation coefficient obtained after wavelet decomposition not match the fft of the original signal in the low-frequency region, resulting in an unsmooth frequency response between the two and varying with the original signal. Is using FFT to solve frequency response unreliable?
clearvars;close all;clc;
fs=10;
dt=1/fs;
t=dt:dt:200;
N=length(t);
signal=(0.2)*randn(1,N);
Max_level=wmaxlev(length(signal),’db10′);
[C,L]=wavedec(signal,Max_level,’fk8′);
level=6;
xL_DWT = wrcoef(‘a’,C,L,’fk8′,level);
xH_DWT=signal-xL_DWT;
%fft
Nfft=length(t);
f_DWT = (1:Nfft/2)*fs/(Nfft);
xL_DWT_fft=fftshift(fft(xL_DWT,Nfft));
xH_DWT_fft=fftshift(fft(xH_DWT,Nfft));
signal_fft=fftshift(fft(signal,Nfft));
wn_low_DWT=xL_DWT_fft./signal_fft;
wn_high_DWT=1-wn_low_DWT;
figure
plot(f_DWT,wn_low_DWT(Nfft/2+1:end));
hold on
plot(f_DWT,wn_high_DWT(Nfft/2+1:end));
ylim([-0.5 2]);
yticks([-0.5:0.5:2])
xlim([0 fs/2^(level-1)]);
xticks([0 fs/2^(level+1) fs/2^(level) fs/2^(level-1)])
xticklabels({‘0′,’fs/2^{i+1}’,’fs/2^{i}’,’fs/2^{i-1}’}) Why does the fft of the component corresponding to the last approximation coefficient obtained after wavelet decomposition not match the fft of the original signal in the low-frequency region, resulting in an unsmooth frequency response between the two and varying with the original signal. Is using FFT to solve frequency response unreliable?
clearvars;close all;clc;
fs=10;
dt=1/fs;
t=dt:dt:200;
N=length(t);
signal=(0.2)*randn(1,N);
Max_level=wmaxlev(length(signal),’db10′);
[C,L]=wavedec(signal,Max_level,’fk8′);
level=6;
xL_DWT = wrcoef(‘a’,C,L,’fk8′,level);
xH_DWT=signal-xL_DWT;
%fft
Nfft=length(t);
f_DWT = (1:Nfft/2)*fs/(Nfft);
xL_DWT_fft=fftshift(fft(xL_DWT,Nfft));
xH_DWT_fft=fftshift(fft(xH_DWT,Nfft));
signal_fft=fftshift(fft(signal,Nfft));
wn_low_DWT=xL_DWT_fft./signal_fft;
wn_high_DWT=1-wn_low_DWT;
figure
plot(f_DWT,wn_low_DWT(Nfft/2+1:end));
hold on
plot(f_DWT,wn_high_DWT(Nfft/2+1:end));
ylim([-0.5 2]);
yticks([-0.5:0.5:2])
xlim([0 fs/2^(level-1)]);
xticks([0 fs/2^(level+1) fs/2^(level) fs/2^(level-1)])
xticklabels({‘0′,’fs/2^{i+1}’,’fs/2^{i}’,’fs/2^{i-1}’}) fft, wavelet, frequency response, decomposition MATLAB Answers — New Questions

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