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Musical-Applications-of-Microprocessors-2ed-Chamberlin-H-1987

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DIGITAL FILTERING 515<br />

INPUT<br />

(C)<br />

-(.9511 Fc/Fs) -(3.751Fc/FS) WHERE:<br />

A, = e AJ ~ e Fe ~ CENTER FREQUENCY OF BAND<br />

-(10.52Fc/Fs) -(41.50Fe/Fs) Fs = SAMPLE RATE<br />

A, = e<br />

Fig. 14-25. (Cont.). (C) 90 degree phase difference network detail.<br />

The other elements are exceptionally easy to implement in digital form.<br />

The frequency <strong>of</strong> the sine and cosine waves entering the multipliers determines<br />

the amount <strong>of</strong> spectrum shift hertz for hertz. As shown, the spectrum<br />

is shifted up, but inversion <strong>of</strong> the driving oscillator phase will cause a<br />

downshift instead. The oscillator is easily implemented with a sine table and<br />

two pointers one-quarter the table length apart. Smooth transitions from<br />

upshift to downshift are accomplished by letting the table increment go<br />

negative, thereby generating "negative" frequencies.<br />

The entire system is operated much like the simpler chorus synthesizer.<br />

Essentially, all <strong>of</strong> the variable elements are fed independent, slowly varying<br />

random signals. Again, adjustment is best done by ear, although many<br />

strange effects are possible by misadjustment.<br />

Interpolation<br />

Virtually everyone was taught in junior high school (before the advent<br />

<strong>of</strong> pocket calculators anyway) how to interpolate in a table <strong>of</strong> logs or trig<br />

functions in order to get an extra digit or two <strong>of</strong> precision. However, in<br />

digital music synthesis, interpolation between waveform table entries or

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