DAFX: Digital Audio Effects, Second Edition

7.3 Phase Vocoder Implementations

This section describes several phase vocoder implementations for digital audio effects. A useful representation is the time-frequency plane where one displays the values of the magnitude |X(n, k)| and phase of the signal. If the sliding Fourier transform is used as an analysis scheme, this graphical representation is the combination of the spectrogram, which displays the magnitude values of this representation, and the phasogram, which displays the phase. However, phasograms are harder to read when the hop size is not small. Figure 7.6 shows a spectrogram and a phasogram which correspond to the discrete-time and discrete-frequency plane achieved by a filter bank (see Figure 7.4) or a block-by-block FFT analysis (see Figure 7.5) described in the previous section. In the horizontal direction a line represents the output magnitude |X(n, k)| and the phase of the kth analysis bandpass filter over the time index n. In the vertical direction a line represents the magnitude |X(n, k)| and phase for a fixed time index n, which corresponds to a short-time spectrum ...