MLSP Fall 2016: Homework 1
Matlab Instructions

Computing the spectrogram

Download the following matlab files: [stft.m]

“stft.m” computes the complex spectrogram of a signal.

You can read a wav file into matlab as follows:

[s,fs] = audioread('filename');
s = resample(s,16000,fs);

Above, we resample the signal to a standard sampling rate for convenience. Next, we can compute the complex short-time Fourier transform of the signal, and the magnitude spectrogram from it, as follows. Here we use 2048 sample windows, which correspond to 64ms analysis windows. Adjacent frames are shifted by 256 samples, so we get 64 frames/second of signal.

To compute the spectrogram of a recording, e.g. the music, perform the following.

spectrum = stft(s',2048,256,0,hann(2048));
music = abs(spectrum);
sphase = spectrum ./(abs(spectrum)+eps);

This will result in a 1025-dimensional (rows) spectrogram, with 64 frames(columns) per second of signal.

Note that we are also storing the phase of the original signal. We will need it later for reconstructing the signal. We explain how to do this later. The eps in this formula ensures that the denominator does not go to zero.

You can compute the spectra for the notes as follows. The following script reads the directory and computes spectra for all notes in it.

notesfolder = 'notes15/';
listname = dir([notesfolder '*.wav']);
notes = [];
for k =1:length(listname)
    [s,fs] = audioread([notesfolder listname(k).name]); 
    s = s(:,1);
    s = resample(s,16000,fs);
    spectrum = stft(s',2048,256,0,hann(2048));
    % Find the central frame
    middle = ceil(size(spectrum,2)/2);
    
    note = abs(spectrum(:,middle));
    % Clean up everything more than 40db below the peak
    note(find(note < max(note(:))/100)) = 0;
    note = note/norm(note); %normalize the note to unit length

    notes = [notes,note];
end

The “notes” matrix will have as many columns as there are notes (15 in our data). Each column represents a note. The notes will each be represented by a 1025 dimensional column vector.

Reconstructing a signal from a spectrogram

reconstructedsignal = stft(reconstructedmagnitude.*sphase,2048,256,0,hann(2048));