of Microprocessors

DIGITAL TONE GENERATION TECHNIQUES
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Table 13--3. FFT Synthesis Example: Sequence of Object Spectrums
Record
number Hrm. Amp. Phase Hrm. Amp. Phase Hrm. Amp. Phase Hrm. Amp. Phase
1 All 0
2 6 1.0 0.85
3 6 1.3 0.85
4 6 1.0 0.00
5 6 1.0 0.15
6 6 1.0 0.30 2 0.5 0.05
7 6 1.0 0.45 2 0.75 0.10
8 6 1.0 0.60 2 1.0 0.15
9 6 0.75 0.65 2 0.60 0.35 9 0.235 0.00 0 0.30 0.20
10 6 0.20 0.60 3 0.10 0.20 9 0.309 0.50 9 0.70 0.40
11 9 0.951 0.50 0 1.0 0.60
12 9 0.809 0.50 0 1.0 0.80
13 9 0.000 0.00 0 1.0 0.00
14 9 0.162 0.00 0 1.0 0.20
15 0 1.0 0.40
16 0 1.0 0.60
Note that all harmonics not specifically listed are assumed to have zero amplitude.
Other Digital Tone Generation Techniques
The tone-generation techniques described up to this point have all been
direct, that is, a straightforward application of digital technology to
generating very precise arbitrary waveforms (table lookup) or very precise
arbitrary spectrums (Fourier synthesis). Either, with allowance for smooth
parameter changes, is theoretically capable of synthesizing any kind of tone.
While these methods are therefore completely general, a lot of"data" must be
"input" to the generator to produce what often seem to be simple changes in
a tone's timbre.
Recall from Chapter 3 that analog FM synthesis was capable of
producing a wide variety of tone colors by manipulating only two synthesis
parameters: the modulation index and the ratio of modulating to carrier
frequencies. Since only two variables were being controlled, the "data rate"
needed by FM synthesis to produce dramatic timbre variations was very low.
FM, however, is not a direct technique, since there is no simple relationship
between the "data" (modulation index and frequency ratio) and either the
waveform or the spectrum. It is also not a general technique, at least in its
pure form, because it cannot synthesize any arbitrary waveform or spectrum.
For the remainder of this chapter, we will look at FM and other indirect
digital synthesis techniques that in many applications have substantial
advantages over direct techniques.
FM Synthesis
FM synthesis is as easily implemented in digital form as it is in analog
form. Furthermore, it is efficient in its use of memory space and computing