Somehow this didn’t make it to the blog after the lecture…

**Classic “concrete” techniques**

- With classic tape techniques, the only way to change the duration of a recorded sound is to change the speed of the tape. (Which also changes pitch.)
- Same is true if all you want is a pitch change. (Duration changes)

**Computer processing techniques**

Software offers two different options for changing duration independent of pitch:

- Granular Synthesis, a process that slices (windows) time domain audio into very small (1 – 100 ms) segments, and
- Phase Vocoding, a process that converts time domain audio into frequency domain representations.

**Converting Domains**

Any arbitrary periodic signal can be represented as a sum of many simultaneous sine waves.

*Fourier Transform*

- Converts a time-domain representation into a frequency domain representation

*Inverse Fourier Transform
*

- Converts a frequency-domain representation into a time domain representation

**Fast Fourier Transform (FFT)**

- The FFT takes a slice of time (a window) that is
*n*samples in length, where n = some-power-of-2. - The number of samples in an FFT window = the number of frequency bands between 0 Hz and the Sampling Rate.
- Only half the bands are usable. (why?)

**How Phase Vocoding Works**

- Each FFT window represents a frame, or still picture, of analysis information (frequency domain content)
- Time compression or expansion involves changing the playback rate of the frames (the conversion of frequency domain to time domain), which takes place during an inverse Fast Fourier Transform (iFFT)
- Like changing the playback rate of film or video.
- Pitch Shifting is an independent process.
- X times all frequency bands (2 = octave up; 0.5 = octave down.

**Phase Vocoding parameters
**

- FFT size (window size)
- Determines number of frequency bands
- Determines length of time per analysis window ( FFT_Size / SR = Length in seconds)

- Number of Overlaps
- Determines onset of windows
- Helps with time resolution

- Window type
- Describes the amplitude envelope applied to each time window
- Can affect accuracy of measurements
- For now, you can stick to a
*Hamming*window

- Time Scale (constant or function)
- Pitch Scale (constant or function)

**Problems with the Phase Vocoder**

- Frequency/Time trade-off – the Uncertainty principle
- the more accurate you are measuring one parameter, the less accurate you are measuring the other.
- Larger FFT size provides more frequency bands, but less information about start time of events, and vice versa.

- Frequency bands are linearly spaced, but our perception of pitch is logarithmic.
- Fourier Transform theory assumes a periodic signal.
- Periodic signals have no beginning or end (infinity in both directions)
- Implied in this assumption (as it relates to the FFT) is that a signal begins its period at the beginning of an analysis window, and that the end of the analysis window is a period end point of the signal. Windowing corrects for the unlikelihood of this happening.

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