Spectral Centroid in Audio

The center of mass of the spectrum.

x(n) is the magnitude of bin number, f(n) is the center frequency of that bin. The following MATLAB function is from the exchange website;

function C = SpectralCentroid(signal,windowLength, step, fs)
signal = signal / max(abs(signal));
curPos = 1;
L = length(signal);
numOfFrames = floor((L-windowLength)/step) + 1;
H = hamming(windowLength);
m = ((fs/(2*windowLength))*[1:windowLength])';
C = zeros(numOfFrames,1);
for (i=1:numOfFrames)
    window = H.*(signal(curPos:curPos+windowLength-1));    
    FFT = (abs(fft(window,2*windowLength)));
    FFT = FFT(1:windowLength);  
    FFT = FFT / max(FFT);
    C(i) = sum(m.*FFT)/sum(FFT);
    if (sum(window.^2)<0.010)
        C(i) = 0.0;
    end
    curPos = curPos + step;
end
C = C / (fs/2);