
194 Audio Effects: Theory, Implementation and Application
found in [2]. Though there is no single best solution for all cases; in phase
vocoder audio effects Hann and Hamming windows are frequently used.
To apply a window function, the input signal is multiplied by the window.
The window function can be offset in time to isolate different regions of the
input signal:
xmnxnw
window
[,][][
(8.3)
where m is the offset of the window. The samples from m to m + N – 1 will be
isolated by the window function, with all other samples set to zero.
Analysis: Fast Fourier Transform
The FFT is an algorithm for calculating the discrete Fourier transform (D ...