## 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
• frequency $$f_s=1000$$ {Hz],
• sampling rate $$T_s:=\dfrac{1}{f_s}=\dfrac{1}{1000}$$ [sec],
• number of samples $$L=12000$$,
• total time $$12$$ [sec].
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