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# Sound Synthesis - PowerPoint PPT Presentation

Sound Synthesis. Part II: Oscillators, Additive Synthesis & Modulation. Plan. Simple Oscillator (wavetable) Envelope control Simple Instrument (Helmholtz) Additive Synthesis Modulation Summary. AMP. FREQ. PHASE. WF. Simple Oscillator. Oscillator 3 strategies.

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## PowerPoint Slideshow about 'Sound Synthesis' - tannar

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Presentation Transcript

### Sound Synthesis

Part II: Oscillators, Additive Synthesis & Modulation

• Simple Oscillator (wavetable)

• Envelope control

• Simple Instrument (Helmholtz)

• Modulation

• Summary

AMP

FREQ

PHASE

WF

Oscillator

3 strategies

Mathematical equation based oscillator

Wavetable oscillator

IIR-Based oscillator

• Solve math function for each sample

• Ex: y = sin(x)

• + Accurate

• Inefficient

•  Non real-time applications

• Pre-computed and stored in memory

• + Fast (Look-up table)

• Memory

Unstable filter that generates waveform of desired amplitude and frequency.

+ Fast

+ Memory efficient

 Sound synthesis

• Example of a wavetable (N = 16)

• Store N values sampled over one cycle

• Phase increment: SI=N f0/fs

Wavetable Oscillator (example)

• Parameters

• N = 16

• F0 = 220

• Fs = 1kHz

• SI = 16 * 220/1000SI = 3.52

• Increase quality:

• Increase sampling rate

• interpolate

Wavetable Oscillator Distortions

• Quantization:Eg, pure tone F0=440Hz, Fs=8,192Hz

• Truncate N=16

• Truncate N=32

• Truncate N=512

• Interpolation: truncate, mean, linear

• Aliasing

Wavetable OscillatorInterpolation

• Truncation (0th level interpolation)

Wavetable Oscillator Interpolation (2)

• Rounding (slightly better 0th order)

Wavetable Oscillator Interpolation (3)

• Linear (First order interpolation)

Wavetable Oscillator – Interpolation (4)

Wavetable Oscillator Interpolation (5)

• Cubic (Third order interpolation)

Wavetable Oscillator Interpolation (6)

• Signal to (interpolation) Noise Ratio (SNR)(eg, pure tone F0=220Hz, Fs=8,192Hz)

• Truncation: SNR = 6 k – 11 dB

• Rounding: SNR = 6 k – 5 dB

• Linear: SNR = 12 (k – 1) dB(Moore, 1977; Hartman, 1987)(k = log2(N) and N is the table length)

• Conclusion: For increasing quality, increase number of samples, and use interpolation.

Wavetable Oscillator Interpolation (7)

• Pure tone F0=440Hz, Fs=8,192Hz

• Truncate N=16

• Truncate N=32

• Truncate N=512

Wavetable Oscillator – Aliasing

• Aliasing: One of the biggest problem for modern digital sound synthesisers (sampling freq fs=48kHz, Nyquist freq fn=fs/2=24kHz).

• How to avoid aliasing?

• Storing a band-limited version of the waveform in the table (in memory)

• Or, generate an aliasing-free signal from frequency-limited Fourier series representation.

• Several sinusoids can fit a set of samples.

• Aliasing when sampling rate is low! Example:

• Signal:f0 = 0.9Hz(red)

• Sampling at:fs = 1Hz, Nyquist freq fn = 0.5Hz

• perceived fa=|n*fs-f0|=0.1Hz(blue) (n such that fa < fn)

• Square wave, 563 Hz fundamental, 48kHz sampling rate.

Generated using “perfect” square waveform

Generated using a limited Fourier series.

• Simple Oscillator (wavetable)

• Envelope control

• Simple Instrument (Helmholtz)

• Modulation

• Summary

AMP

FREQ

PHASE

WF

• Attack

• Decay

• Sustain

• Release

• Important is:

• Duration

• Shape

• Linear

• Exponential

• Other (functional, table)

Linear vs. Exponential Envelope

A) Linear

B) Exponential

• Recall:“amplitude perception is (nearly) logarithmic”

• linear decay  logarithmic (perceived) fading

• Exponential decay  linear (perceived) fading

• Note: Exponential decay never reaches zero  set min value

A

fm

• wavetable interpolated shape.

• Easy encoding of several repetitions.

• Drawback:

• attack and decay times are affected by overall duration!

• Alternative:

• interpolated function generator

fc

• Simple Oscillator (wavetable)

• Envelope control

• Simple Instrument (Helmholtz)

• Modulation

• Summary

AMP

FREQ

PHASE

WF

• Helmholtz model

• Waveform

• Constant frequency

• Envelope

• Envelope feeds varying amplitude to the oscillator.

AMP

DURATION

ATTACK

DECAY

ASD Envelope

FREQ

AMP

PHASE

• Envelope generator used as a signal processor.

• Oscillator feeds varying amplitude to the envelope generator.

• Allows to process the amplitude of a natural (recorded) sound through an envelope.

AMP

FREQ

PHASE

DURATION

AMP

ATTACK

DECAY

ASD Envelope

• Helmholtz model

• Waveform

• Constant frequency

• Envelope

• Limitations:

• Amplitudes of all spectral components vary simultaneously.

• All spectral components are perfect (integer) harmonics.

• ... unlike real sounds!

AMP

DURATION

ATTACK

DECAY

ASD Envelope

FREQ

AMP

PHASE

• Simple Oscillator (wavetable)

• Envelope control

• Simple Instrument (Helmholtz)

• Modulation

• Summary

AMP

FREQ

PHASE

WF

FREQ

FREQ

FREQ

+

• Analysis: Frequency and amplitude envelopes can be obtained from analysis (spectrogram)

• Flexibility: Virtually any sound can be synthesised.

• Allows for the generation of new, natural sounding functions.

• Quality: Can realize sounds that are “indistinguishable from real tones by skilled musicians” (Risset, Computer Study of Trumpet Tones, 1966)

• But...

• Require large amount of data to describe a sound

• Each oscillator requires two functions

• Functions are only valid for limited rangeof pitch and loudness!

• Analysis for a given pitch and loudness will not give the same timbre when extrapolated for different pitch and loudness.

• Requires very large library of function sets!

• Just too much control?

• Simple Oscillator (wavetable)

• Envelope control

• Simple Instrument (Helmholtz)

• Modulation

• Summary

AMP

FREQ

PHASE

WF

• Modulation:“Alteration of amplitude, phase or frequency of an oscillator, in accordance to another signal” (Dodge & Jerse, 1997)

• Vocabulary:

• Carrier oscillator: modulated oscillator

• Carrier wave: modulated signal (prior to modulation)

• Spectral components of modulated signal:

• Carrier components: come only from carrier

• Sidebands: come from both carrier & modularion

• Carrier:

• Frequency: fc

• Modulating

• Frequency: fm

• Amplitude m*AMP

• Modulation index: m

• m=0 no modulation

• m>0 modulation

• m=1 full modulation

m*AMP

AMP

fm

+

fc

AMP

• Carrier frequency fc

• Unaffected by modulation index

• Sidebands fc+/-fm

• Amplitude m/2*AMP

• Energy split equally between lower/higher

• When m=1, sidebands 6dB below carrier

• Perception

• If fm>10Hz -> two tones, additional loudness.

• If fm<10Hz -> tremolo

Amplitude

AMP

m/2*AMP

fc-fm

fc

fc+fm

Frequency

Pure tone fc=220Hz

Tremolo fc=220Hz, fm=6Hz, m=1

A

A

A

fm

fc

fm

• Modulation is applied directly to carrier’s amplitude.

• A=0  no signal!

• Alters frequency!

• If both sinusoidals:

• Only sidebands:fc-fm and fc+fm!

• Amplitude A/2

• Eq. to signal multiplication

fc

*

Amplitude

A/2

fc-fm

fc

fc+fm

Frequency

• Modulating signal applied to the carrier’s frequency.

• “Slight wavering of pitch”

• Pitch varying between fc-v <= fv <= fc+v

• Average is <fv> = fc

• Eg, fc=220Hz

• Pure tone

• Vibrato fv=6Hz, v=0.05fc

v

fm

fc

+

A

fv

• Simple Oscillator (wavetable)

• Envelope control

• Simple Instrument (Helmholtz)

• Modulation

• Summary

AMP

FREQ

PHASE

WF

• C. Dodge, C., & Jerse, T. A. (1997). Computer Music: Synthesis, Composition, and Performance. Schrimer, UK.(see chapter 4)

fc

fm

AMP

DURATION

ATTACK

DECAY

ASD Envelope

+

fv

AMP

DURATION

ATTACK

m*AMP

ASD Envelope

fm

AMP

+

fc

AMP