of Microprocessors

464 MUSICAL ApPLICATIONS OF MICROPROCESSORS
Fig. 13--24. Waveform computed from sequence of object spectrums from
Tables 13--2 and 13--3.
expressed as multiples of the inverse of the record size (39 Hz for lO-ks/s
sample rate and 256 record size) and amplitude is in arbitrary units. Table
13-3 is a listing of the nonzero portion of the corresponding FFT spectrum
sequence.
Figure 13-24 is the actual waveform (with line segments connecting
the sample points for easier visualization) created by this sequence. Note that
ultrasharp attacks are simply not possible with FFT synthesis. In fact, no
event shorter than a record period can be resolved. This drives home the
primary assumption of FFT synthesis that the record size must be shorter
than the limits of human time perception yet longer than the limits of
human frequency perception for simultaneous tones.
Table 13--2. FFT Synthesis Example: Source Spectrum Sequence
Record
number Freq. Amp. Freq. Amp. Freq. Amp. Freq. Amp. Freq. Amp.
1 0 0
2 5.7 1.0
3 6.0 1.3
4 6.3 1.0
5 6.3 1.0
6 6.3 1.0 2.1 0.5
7 6.3 1.0 2.1 0.75
8 6.3 1.0 2.1 1.0
9 6.1 0.75 2.4 0.6 8.7 0.2 9.3 0.2 0.4 0.3
10 5.9 0.2 2.7 0.1 8.7 0.5 9.3 0.5 0.4 0.7
11 8.7 0.5 9.3 0.5 0.4 1.0
12 8.7 0.5 9.3 0.5 0.4 1.0
13 8.7 0.3 9.3 0.3 0.4 1.0
14 8.7 0.1 9.3 0.1 0.4 1.0
15 0.4 1.0
16 0.4 1.0