How to use the log-binning of the Fourier energy spectrum?

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Ali Nouri 2020-3-15

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评论： Ali nouri 2020-6-26

Hi

Do anybody know, How to use the log-binning of the Fourier energy spectrum?

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Answer 1

Thiago Henrique Gomes Lobato 2020-3-15

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I'm not entirely sure what you mean by log-binning, but a regular interpretation for it is just to resample the fft in log-spaced bins instead of linear ones. A way to do it is to generate your log-frequency bins and then map all linear values to it's respective bins in the log scale. Something like this can do the trick, although it is not 100% optimized:

Fs         = 8000;
t          = 0:1/Fs:0.2;
a          = sin(2*pi*1000*t)+randn(1,length(t));
A          = fft(a);
A          = A.*conj(A);
% Freq vectors
LinearFreq = linspace(0,Fs,length(A));
SizeLogFreq= round(length(A)/4); % Can be, theoretically, any integer
LogFreq    = logspace(1,log10(Fs),SizeLogFreq); 
% Mapping
Alog       = zeros(1,SizeLogFreq);
for idx=1:length(A)
   [~,idxLog]= min(abs(LinearFreq(idx)-LogFreq)); 
   Alog(idxLog) = Alog(idxLog)+A(idx); 
end
figure,
plot(LinearFreq,A)
hold on
plot(LogFreq,Alog)

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Thiago Henrique Gomes Lobato 2020-3-15

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N = length(Del_mat); % Del_mat is matrix of 8760X30
fs = 1;
figure(1)
s=5;
for i=1:30
y(:,i)=Del_mat(:,i);
y1(:,i) = fft(y(:,i));
power(:,i)= abs(y1(:,i)).^2/N;     % power of the DFT
X_mags(:,i)=power(:,i);
X_mags(:,i)=smooth(X_mags(:,i),s);
end
bin_vals = [0 : N-1];
fax_Hz = bin_vals*fs/N;
SizeLogFreq= round(N/4); % Can be, theoretically, any integer
LogFreq    = logspace(1,log10(fs),SizeLogFreq); 
% Mapping
Alog       = zeros(SizeLogFreq,size(Del_mat,2));
for idx=1:N
   [~,idxLog]= min(abs(fax_Hz(idx)-LogFreq)); 
   Alog(idxLog,:) = Alog(idxLog,:)+X_mags(idx,:); 
end
N_2 = ceil(N/2);
for j=1:7
loglog(fax_Hz(1:N_2),X_mags((1:N_2),j))
hold on 
loglog(LogFreq(1:N_2),Alog((1:N_2),j)) % May need to go beyong N/2
end