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Oscillator Algorithm

Oscillator Algorithm. Oscillator Algorithm. SI. Sampling Increment (determines frequency). PHS. Phase Count (0 ≤ PHS < L). Waveform Table. 0. L-1. Output. Sampling Increment. If SI = 1.0:. SR. exp.: 43 Hz = 44100 / 1024. freqF =. L. To create a specific target frequency:. freqT.

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Oscillator Algorithm

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  1. Oscillator Algorithm

  2. Oscillator Algorithm SI Sampling Increment (determines frequency) PHS Phase Count (0 ≤ PHS < L) Waveform Table 0 L-1 Output

  3. Sampling Increment If SI = 1.0: SR exp.: 43 Hz = 44100 / 1024 freqF = L To create a specific target frequency: freqT SI = exp.: 10.23 = 440.0 / 43 freqF Or: L * freq. SI = SR

  4. Oscillator Stages L * frequency Initialization: SI = SR PHS = 0 or other initial value PHS = (PHS + SI)%L Sample Rate: IPHS = int(PHS) OUT = WAVE(IPHS) …… etc.

  5. General Stages Initialization: Control rate: Sample Rate: once every n samples SR / second

  6. Program Flow init: control: sample: t

  7. Oscillator Detail SI int fract Waveform Table + 0 PHS int fract 1 = 2 result int fract 3 4 index = (int)PHS 5 N bits n bits ……… 2N = L L-1 (210 = 1024)

  8. N bits n bits n determines the frequency accuracy Df n 0 4 8 12 16 43.066 2.692 0.168 0.0105 0.000657 SR = 44100 L = 1024 How much accuracy is necessary?

  9. L oscillator interpolated 256 512 1024 2048 36 42 48 54 84 96 108 120 dB dB Signal to Noise Depends on L & method Trade-off

  10. Interpolating Oscillator wavetable M M+1 nT int fract output = wavetable(M) + fract*(wavetable(M+1)-wavetable(M))

  11. Envelope Generator Specification LevelScale TimeScale Env.type EnvGen Frequency Mul: Amp Wavetable Osc signal

  12. Envelope Multiplication Osc t * EnvGen t = result t

  13. Env: Changing Amplitude Type: ADSR Attack Decay amp Sustain Release t 0 peakLevel sustainLevel sustainLevel 0 attackTime decayTime sustainTime releaseTime Specification:

  14. Envelope Scaling peak amplitude t duration peak amplitude t duration

  15. Real Instruments Effort ff high t mf med. t p low t

  16. Interpolation by Sample amp(L+1) amp amp(L) n nT L L+1 N n amp =amp(L)+ (amp(L+1)-amp(L)) N + = * / operations count: 1 1 1 1

  17. Interpolation by Successive Addition amp(L+1) amp amp(L) n nT N initialization:amp=amp(L) (amp(L+1)-amp(L)) Damp = N loop:amp=amp + Damp (N times!) + = * / operations count: 1 0 0 0

  18. Interpolation by Successive Multiplication amp(L+1) amp amp(L) n nT N initialization:amp=amp(L) Amp(L+1) Damp = 10 pow( log ( ) - log (Amp(L)) ) N loop:amp=amp * Damp (N times!) + = * / operations count: 0 0 1 0

  19. Problems discontinuities amp nT

  20. Changing Amplitude at low Control Rate Very Audible! sample interpolation frame interpolation nT Discontinuity!

  21. Discontinuities in Samples t Sample hold for 2 sampling instances! Audible Click

  22. Discontinuities in Phase/Frequency f t a t Very Audible

  23. SuperCollider control rate 44100 kr = = 689 Hz 64 block rates? 44100 = 43 Hz 1024 44100 = 86 Hz 512 44100 = 344 Hz 128

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