of Microprocessors

SOURCE-SIGNAL ANALYSIS 565
overlapped sample data, it must not alter the data itself because some of it
will be needed for overlapping purposes in the next spectral frame. Likewise,
the FFT will destroy the sample data unless a copy is made and the copy
transformed. For maximum efficiency, one can combine copying, windowing,
and bit-reverse decimation into one program loop that takes little more
time than windowing alone. If memory space is tight, the samples that ate
not needed in the next frame may be destroyed.
In summary, the procedute for converting a stting of samples into a
string of spectra is as follows (512-point FFT and 2: 1 ovetlap):
1. Discard 256 signal samples ftom' the right half of the analysis record.
2. Copy (or equivalent) the remaining 256 samples ftom the left to the
right half of the analysis record.
3. Accept 256 new signal samples from the input string and put them in
the left half of the analysis record.
4. Make a copy of the analysis record.
5. Apply the chosen window to the copy.
6. Do a 512-point real FFT.
7. The 256 sine and cosine components represent one spectral frame. They
may be stored as is or processed further.
8. Go to step 1 for the next spectral ftame.
Note that twice as much output data is generated as input data if phase
information is retained. This is a result of oversampling (overlapping), but as
will be seen later such oversampling simplifies subsequent spectral processing.
In fact, for analysis-resynthesis applications, it may be necessary to
further oversample the sequence of spectra to obtain good resynthesis quality
after modification.
Spectral Processing
In the previous section, two methods of obtaining the time-varying
spectrum of a sound were presented. We can now assume that the spectrum
is in the form of a sequence of frames at the spectral sample rate and each
frame contains samples (in frequency) of the spectral curve at a point in time.
Three primary applications exist for the spectral data. The first is direct
modification of the spectrum and immediate FFT resynthesis as sound. The
second, which may be considered an extension of the first, is the extraction of
one or more time-varying parameters, such as fundamental frequency or gross
spectral shape. These data may then be used to control conventional synthesis
equipment such as oscillators, filters, etc., rather than direct reconstruction
with the FFT. The third application is display and subsequent study in an
effort to learn more about the processes that created the original sound.
Often, it is convenient to perform some translation of the spectral data
before it is modified. If the FFT was used for analysis, each time-frequency