of Microprocessors

SOURCE-SIGNAL ANALYSIS
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Fig. 16-12. Spectrum frequency manipulations. (A) Unmodified spectral data.
(8) Spectrum shift upward. (C) Frequency interpolation. (D) Left:
Linear compression of interpolated spectrum. Right: Resampling
at original center frequencies.
Besides amplitude modification of the spectral components, many
weird and wonderful things can be accomplished by altering their frequencies
as in Fig. 16-12. If, for example, the spectral frequency resolution is 39 Hz,
an upward spectrum shift of 39 Hz can be accomplished simply by shifting
the numbers in each frame upward one slot. The dc frequency band would be
replaced by zero and the highest band would be discarded. Likewise, the
spectrum may be shifted downward without the reflection around zero that
analog frequency shifters suffer from. Circular shifting and spectral inversion
are also easily accomplished.
For maximum flexibility in frequency alteration, it is necessary to
interpolate between the tabulated frequencies. The same techniques used for
time interpolation in Chapter 13 can be used for frequency interpolation in a
spectral frame. With suitable interpolation, the spectral curve can be regarded
as continuous (infinite sample rate in frequency) and frequency shifts
of any arbitrary amount may be performed.
Instead of shifting all frequencies by an equal amount, which usually
converts harmonic tones into inharmonic ones, the spectrum can be linearly