1. Gerald Leung

2.  Implementation Goal of Phase Vocoder  Spectral Analysis and Manipulation  Matlab Implementation  Result Discussion and Conclusion

3.  Time Stretch ◦ Unwrap phase and calculate the Magnitude and Phase increment per sample in analysis grid ◦ Interpolate the synthesis phase response using phase increments calculated from analysis grid in previous step ◦ Re-construct the audio signal using a weighted sum of cosine functions using the interpolated synthesized magnitude and phase as cosine parameters  *** IFFT Operation ***

4.  FFT of a window function is represented as a series of Sine and Cosine Functions http://zone.ni.com/devzone/cda/tut/p/id/3342

5.  Given the interpolated phase and magnitude, we can re-construct the signal from frequency domain for each window segment  Overlap add the interpolated window segment using the same hope size window in the analysis grid

6.  Similar Concept as Time Stretching ◦ Take FFT of each window segment and calculate the magnitude and phase increment per sample (FFT bin) ◦ Multiply the phase increment by a transposition factor ◦ Interpolate the synthesis signal using transposed phase increments from previous step ◦ Re-construct the signal from the frequency domain using weighted sum of cosine functions with interpolated phase and magnitude as parameters

7.  Zero-phase every FFT bin  Take the IFFT of the magnitude of FFT bin for signal re-construction

8.  Same concept as Robotization  Randomize the phase instead

9.  Maintain loud parts of the signal  Attenuate low parts of the signal  Modify the magnitude, maintain the phase grain = in_signal(pin+1:pin+WLen).*w1; f = fft(grain); r = abs(f); ft = f.*r.^2./(r+coef);

11.  Not Completely free of artifact free ◦ Mathematically impossible to express the exact spectrum ◦ Phasiness, reverbation etc

12.  Large windows causes “smearing” effect  Smaller windows ◦ Less frequency resolution ◦ Minimum frequency is more restricted  Less bass