of Microprocessors

568 MUSICAL ApPLICATIONS OF MICROPROCESSORS
stretched or compressed. For example, if all of the frequencies were multiplied
by two (with those beyond the high-frequency limit thrown away),
then the pitch of the sound when resynthesized would be raised an octave, but
the timing and waveform (except for high-frequency rolloff due to discarded
components) would remain unchanged! One can also nonlinearly stretch,
compress, and otherwise distort the distribution of the spectral curve without
affecting the amplitudes of the peaks and valleys themselves. All of these
manipulations can, of course, be time varying. After processing, the spectral
curve is resampled at the original center frequencies and resynthesized. Note
that severe compression of the spectrum may lead to local "alias distortion"
when it is resampled for synthesis.
Time alteration of the sequence of spectrum frames is also possible with
equally strange-sounding results. In time modification, each spectral component
in the frame is considered as a time sample of the amplitude curve of
that component. If the entire set of spectral data is viewed as a rectangular
array with time in the X direction and frequency in the Y direction, then this
is equivalent to thinking in terms of rows rather than columns.
The simplest manipulation is horizontal stretching or compression of
the sequence, which amounts to slowing or speeding of the sound events
without affecting the frequency or timbre. Time interpolation between the
spectral values can be used to implement any arbitrary amount of speed
change. When resynthesized, the modified spectrum is resampled ar the
original time points.
The dispersive filter mentioned earlier may be simulated by shifting the
rows of spectral data with respect to each other such rhat the lower-frequency
rows are delayed more than the higher-frequency rows. Reverse dispersion in
which high frequencies are delayed more is also possible as well as nonlinear
dispersion. Small amounts of dispersion are most effective with percussive
sounds, while larger amounts affect all but the most steady of tones. Vocals
in particular are given strange accents by dispersion.
Since the spectral data are being considered as a set of simultaneously
varying waveforms, it is obvious that these waveforms may themselves be
filtered. Uniform low-pass filtering of all of the bands simply blurs rapid
changes in the spectrum, thus making vocals, for example, sound drunk.
High-pass filtering, on the other hand, emphasizes rapid changes and may
produce a "caricature" of the original sound. Resonant low-pass filtering
with moderate Q factors preserves the steady states of the spectrum but gives
any rapid changes a "twangy" quality due to the overshoot and ringing of the
filter. Of course, each frequency band can be filtered differently, which tends
to combine filtering and dispersion effects.
Resynthesis
In Chapter 13, direct synthesis from amplitude and frequency data
using the FFT was described. Basically, the procedure consisted of conversion