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)
