Download presentation

Presentation is loading. Please wait.

Published byJulianna Dunnaway Modified over 3 years ago

2
Sound Synthesis Part II: Oscillators, Additive Synthesis & Modulation

3
Plan Simple Oscillator (wavetable) Envelope control Simple Instrument (Helmholtz) Additive Synthesis Modulation Summary WF AMPFREQ PHASE

4
Simple Oscillator Oscillator 3 strategies 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

5
Wavetable Oscillator Example of a wavetable (N = 16) Store N values sampled over one cycle Phase increment: SI=N f0/fs

6
Wavetable Oscillator (example) Parameters –N = 16 –F0 = 220 –Fs = 1kHz –SI = 16 * 220/1000 SI = 3.52 Increase quality: –Increase sampling rate –interpolate

7
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

8
Wavetable Oscillator Interpolation Truncation (0 th level interpolation)

9
Wavetable Oscillator Interpolation (2) Rounding (slightly better 0 th order)

10
Wavetable Oscillator Interpolation (3) Linear (First order interpolation)

11
Wavetable Oscillator – Interpolation (4) Quadratic (Second order interpolation)

12
Wavetable Oscillator Interpolation (5) Cubic (Third order interpolation)

13
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.

14
Wavetable Oscillator Interpolation (7) Pure tone F0=440Hz, Fs=8,192Hz –Truncate N=16 –Truncate N=32 –Truncate N=512

15
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.

16
Aliasing (2) 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)

17
Aliasing (3) Square wave, 563 Hz fundamental, 48kHz sampling rate. Generated using “perfect” square waveform Generated using a limited Fourier series.

18
Plan Simple Oscillator (wavetable) Envelope control Simple Instrument (Helmholtz) Additive Synthesis Modulation Summary WF AMPFREQ PHASE

19
Time Envelope (1) ADSR Envelope –Attack –Decay –Sustain –Release Important is: –Duration –Shape Linear Exponential Other (functional, table)

20
Linear vs. Exponential Envelope 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) LinearB) Exponential

21
Oscillator as an Envelope Generator Advantages: –wavetable interpolated shape. –Easy encoding of several repetitions. Drawback: –attack and decay times are affected by overall duration! Alternative: –interpolated function generator fc A fm

22
Plan Simple Oscillator (wavetable) Envelope control Simple Instrument (Helmholtz) Additive Synthesis Modulation Summary WF AMPFREQ PHASE

23
Simple Instrument Helmholtz model –Waveform –Constant frequency –Envelope Envelope feeds varying amplitude to the oscillator. ASD Envelope AMP FREQ PHASE AMP ATTACK DURATION DECAY

24
Simple Instrument (2) 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. AMPFREQ PHASE ASD Envelope AMP ATTACK DURATION DECAY

25
Limitations of the Simple Instrument Helmholtz model –Waveform –Constant frequency –Envelope Limitations: –Amplitudes of all spectral components vary simultaneously. –All spectral components are perfect (integer) harmonics.... unlike real sounds! ASD Envelope AMP FREQ PHASE AMP ATTACK DURATION DECAY

26
Plan Simple Oscillator (wavetable) Envelope control Simple Instrument (Helmholtz) Additive Synthesis Modulation Summary WF AMPFREQ PHASE

27
Types of synthesis Sound Synthesis Additive synthesis Distortion techniques Subtractive synthesis Granular synthesis Analysis based Physical modelling

28
Additive Synthesis FREQ +

29
Additive Synthesis (2) 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)

30
Additive Synthesis (3) But... –Require large amount of data to describe a sound Each oscillator requires two functions –Functions are only valid for limited range of 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?

31
Plan Simple Oscillator (wavetable) Envelope control Simple Instrument (Helmholtz) Additive Synthesis Modulation Summary WF AMPFREQ PHASE

32
Modulation 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

33
Amplitude Modulation Carrier: –Frequency: fc Modulating –Frequency: fm –Amplitude m*AMP Modulation index: m –m=0 no modulation –m>0 modulation –m=1 full modulation AMP fc m*AMP fm AMP +

34
Amplitude Modulation (2) 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 tremolo m/2*AMP AMP fc-fmfc+fmfc Amplitude Frequency Pure tone fc=220Hz Tremolo fc=220Hz, fm=6Hz, m=1

35
Amplitude Modulation (3)

36
Ring Modulation 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 A fm A/2 fc-fmfc+fmfc Amplitude Frequency fc A fm A *

37
Vibrato Modulation Modulating signal applied to the carrier’s frequency. “Slight wavering of pitch” Pitch varying between fc-v <= fv <= fc+v Average is = fc Eg, fc=220Hz –Pure tone –Vibrato fv=6Hz, v=0.05fc fc fm A + v fv

38
Vibrato Modulation (2)

39
Plan Simple Oscillator (wavetable) Envelope control Simple Instrument (Helmholtz) Additive Synthesis Modulation Summary WF AMPFREQ PHASE

40
Additional Reading C. Dodge, C., & Jerse, T. A. (1997). Computer Music: Synthesis, Composition, and Performance. Schrimer, UK. (see chapter 4)

41
fc fm + v fv ASD Envelope AMP ATTACK DURATION DECAY

42
AMP fc m*AMP fm + ASD Envelope AMP ATTACK DURATION

Similar presentations

OK

Digital Oscillators. Everything is a Table A table is an indexed list of elements (or values) A digital oscillator or soundfile is no different.

Digital Oscillators. Everything is a Table A table is an indexed list of elements (or values) A digital oscillator or soundfile is no different.

© 2018 SlidePlayer.com Inc.

All rights reserved.

By using this website, you agree with our use of **cookies** to functioning of the site. More info in our Privacy Policy and Google Privacy & Terms.

Ads by Google

Ppt on non biodegradable wastes Ppt on data handling for grade 6 Upload and view ppt online ticket Ppt on telephone etiquettes Ppt on spiritual leadership model Ppt on 2 stroke ic engineering Ppt on centring ig Ppt on regional transport officer Ppt on conference call etiquette at the office Ppt on sources of water