A phase vocoder is a type of vocoder-purposed algorithm which can interpolate information present in the frequency and time domains of audio signals by using phase information extracted from a frequency transform. The computer algorithm allows frequency-domain modifications to a digital sound file (typically time expansion/compression and pitch shifting). At the heart of the phase vocoder is the short-time Fourier transform (STFT), typically coded using fast Fourier transforms. The STFT converts a time domain representation of sound into a time-frequency representation (the "analysis" phase), allowing modifications to the amplitudes or phases of specific frequency components of the sound, before resynthesis of the time-frequency domain representation into the time domain by the inverse STFT. The time evolution of the resynthesized sound can be changed by means of modifying the time position of the STFT frames prior to the resynthesis operation allowing for time-scale modification of the original sound file. Phase coherence problem The main problem that has to be solved for all cases of manipulation of the STFT is the fact that individual signal components (sinusoids, impulses) will be spread over multiple frames and multiple STFT frequency locations (bins). This is because the STFT analysis is done using overlapping analysis windows. The windowing results in spectral leakage such that the information of individual sinusoidal components is spread over adjacent STFT bins. To avoid border effects of tapering of the analysis windows, STFT analysis windows overlap in time. This time overlap results in the fact that adjacent STFT analyses are strongly correlated (a sinusoid present in analysis frame at time "t" will be present in the subsequent frames as well). The problem of signal transformation with the phase vocoder is related to the problem that all modifications that are done in the STFT representation need to preserve the appropriate correlation between adjacent frequency bins (vertical coherence) and time frames (horizontal coherence). Except in the case of extremely simple synthetic sounds, these appropriate correlations can be preserved only approximately, and since the invention of the phase vocoder research has been mainly concerned with finding algorithms that would preserve the vertical and horizontal coherence of the STFT representation after the modification. The phase coherence problem was investigated for quite a while before appropriate solutions emerged. History The phase vocoder was introduced in 1966 by Flanagan as an algorithm that would preserve horizontal coherence between the phases of bins that represent sinusoidal components. This original