STFT, MDCT and inverses. Onset and pitch detection

Short Time Fourier Transform, MDCT and their inverse. CQT. Onset and Pitch detection.

--------------------------------------
Class name : Signal
----------------------------------
handles basic Signal operations and transforms.
* wave loading
* STFT with any window and overlap ratio from 0 to 1
* MDCT and its inverse
* constant Q transform
* splitting into frames
* onset detection
* pitch detection

Main properties that are read/write
* s : signal
* windowLength (ms)
* nfft (samples)
* overlapRatio (>=0 and <1)
* S : stft data

Main properties that are read only :
* sLength : signal length
* nChans : number of channels
* nfftUtil : number of bins in the positive frequency domain
* framesPositions, nFrames : positions and number of frames
* sWin, sWeights : windowed data

example that produced the description figure :

% Create a Signal object from a wav file
s = Signal('linktomyfile.wav');

%set window length to 50ms
s.windowLength = 50;

%set window overlap to 75%
s.overlapRatio = 0.75;

%compute STFT
s.STFT;

%display log-spectrogram
figure(1)
clf
subplot 311
imagesc(10*log10(abs(s.S(1:s.nfftUtil,:,1)).^2));
xlabel('frame')
ylabel('frequency bin')
axis xy
title('spectrogram')

%compute f0 between 200 and 500Hz
pitchs = s.mainPitch(200,500);

%display it
subplot 312
plot(pitchs)
xlabel('frame')
ylabel('f0 (Hz)')
grid on
title('f0 detection')

%Compute onsets that both appear and low and high frequencies
onsets = s.getOnsets(0,500).*s.getOnsets(6000,15000);

%display them
subplot 313
plot(onsets)
xlabel('frame')
ylabel('onset presence')
grid on
title('onset detection')

----------------------------
Note that :
* all properties are automatically set relevantly in case of modifications. for example, when nfft is set, windowLength is changed accordingly
* the pitch detection algorithm is designed to work with a considerable amount of background superimposed to the lead signal. It should hence give reasonable results for popular music. Note that the lead signal ought to be more or less harmonic.