Finite discrete Fourier transform
computer sound

In the present page we analyze audio signal given by \[ x(t) = \sin\bigl(2t(t-3)(t-6)(t-9)(t-12)\bigr), \quad t\in[0,12]. \] We create this as This is NOT comfortable sound. If you do not mind, you can hear its wav file. By using MATLAB we have the graph of \(x(t)\), and its Fourier transform, spectrogram by the MATLAB command, and out original spectrogram. See computer_sound.m, computer_sound_a.m, computer_sound_b.m, computer_sound_c.m and computer_sound_d.m for the detail.
Discrete audio signal Discrete Fourier transform
Discrete Fourier transform (shifted) Spectrogram