Filter-Based Oscillator Algorithms for Virtual Analog Synthesis - - PowerPoint PPT Presentation

▶

Feb 03, 2024 120 likes •353 views

Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria April 4, 2014 http://diss.pekonen.cc/ V + V + + V + V Contents of the presentation Analog synthesizers 1 Digital

SLIDE 1

Filter-Based Oscillator Algorithms for Virtual Analog Synthesis

Jussi Pekonen Lectio Praecursoria

April 4, 2014

http://diss.pekonen.cc/

− + − + V+ V− V+ V−

SLIDE 2

Contents of the presentation

1 Analog synthesizers

2 Digital oscillators and aliasing

3 Antialiasing oscillator algorithms

4 The results of the dissertation publications

5 Summary

Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria, April 4, 2014 http://diss.pekonen.cc/ 2/23

SLIDE 3

Analog synthesizers

Sources of the images: Moog Modular: Mark Smart EMS VCS-3, Oberheim 4, Roland C360, Korg MS-20: Wikipedia Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria, April 4, 2014 http://diss.pekonen.cc/ 3/23

SLIDE 4

Sound example I

Brandenburg Concerto no 3, part Allegro

Album: Switched-On Bach; Player: Wendy (Walter) Carlos The album won three Grammy awards in 1969 One of the first classical music albums that sold over 500,000 copies

Source of the image and sound example: http://en.wikipedia.org/wiki/Switched-On_Bach

Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria, April 4, 2014 http://diss.pekonen.cc/ 4/23

SLIDE 5

Sound example II

Theme music from movie On Her Majesty’s Secret Service

Composer: John Barry First big budget movie that use an analog synthesizer in the theme music

Source of the image: http://www.imdb.com/title/tt0064757/ Source of the sound example: http://www.youtube.com/watch?v=N8XNBpIkQpU

Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria, April 4, 2014 http://diss.pekonen.cc/ 5/23

SLIDE 6

Sound example III

Thriller (single)

Performer: Michael Jackson The most sold single record in the the world “Bass” played with two coupled MiniMoog synthesizers

Source of the image: http://en.wikipedia.org/wiki/Thriller_(song) Source of the sound example: http://www.youtube.com/watch?v=ZEHsIcsjtdI

Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria, April 4, 2014 http://diss.pekonen.cc/ 6/23

SLIDE 7

Sound example IV

”Overworld” theme from the game Super Mario Bros

Composer: Koji Kondo In fact digital subtractive synthesis,

nly source signals without filtering

Source of the image: http://en.wikipedia.org/wiki/File:NES_Super_Mario_Bros.png Source of the sound example: http://www.supermariobrothers.org/music/smb-overworld.mp3

Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria, April 4, 2014 http://diss.pekonen.cc/ 7/23

SLIDE 8

Subtractive synthesis

Source-filter synthesis

Oscillator Filter Output

1 2 3 4 5 Frequency (kHz) 1 2 3 4 5 Frequency (kHz) 1 2 3 4 5 Frequency (kHz)

Spectrally rich source signal Time-varying lowpass filter

Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria, April 4, 2014 http://diss.pekonen.cc/ 8/23

SLIDE 9

Analog oscillator

− + − + V+ V− V+ V−

T0 2T0 −1 1 Time (s) T0 2T0 −1 1 Time (s) T0 2T0 −1 1 Time (s)

Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria, April 4, 2014 http://diss.pekonen.cc/ 9/23

SLIDE 10

Trivial digital oscillators

f0Ts + mod1 p(n) z−1 2 + −1 s(n) p(n) + − P sgn r(n; P) s(n) abs −2 + 1 st(n)

Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria, April 4, 2014 http://diss.pekonen.cc/ 10/23

SLIDE 11

Aliasing in digital oscillators

0.1 0.2 0.3 0.4 0.5 −40 −20 Listen! (Without aliasing) Frequency (× sample rate) Magnitude (dB) Fundamental frequency: 3.263 kHz Sample rate: 44.1 kHz

Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria, April 4, 2014 http://diss.pekonen.cc/ 11/23

SLIDE 12

Bandlimited algorithms

0.1 0.2 0.3 0.4 0.5 −40 −20 Frequency (× sample rate) Magnitude (dB) Additive synthesis Wavetable synthesis Discrete Summation Formulae Inverse FFT synthesis

Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria, April 4, 2014 http://diss.pekonen.cc/ 12/23

SLIDE 13

Quasi-bandlimited algorithms

0.1 0.2 0.3 0.4 0.5 −40 −20 Frequency (× sample rate) Magnitude (dB) Bandlimited impulse train (BLIT) Bandlimited step function sequence (BLEP)

Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria, April 4, 2014 http://diss.pekonen.cc/ 13/23

SLIDE 14

Alias-suppressing algorithms

0.1 0.2 0.3 0.4 0.5 −40 −20 Frequency (× sample rate) Magnitude (dB) Oversampled Filtered full-wave rectified sine Differentiated polynomial waveform

Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria, April 4, 2014 http://diss.pekonen.cc/ 14/23

SLIDE 15

Ad-hoc algorithms

The purpose is to produce signals that resemble the classical waveforms, but not necessarily without aliasing 1 2 −1 1 Time (×T0) Post-processing algorithms (reduce aliasing) Amplitude distortion of a sine Phase distortion of a sine Feedback FM synthesis Bitwise operations applied to a sine

Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria, April 4, 2014 http://diss.pekonen.cc/ 15/23

SLIDE 16

The results of the dissertation publications

Publication I

−2 −1 1 2 0.5 1 −2 −1 1 2 0.5 1 −2 −1 1 2 0.5 1 Time (sample index) −2 −1 1 2 0.5 1 −2 −1 1 2 0.5 1 −2 −1 1 2 0.5 1 Time (sample index) Generalization of the polynomial-based BLEP algorithm Reduces aliasing a lot

Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria, April 4, 2014 http://diss.pekonen.cc/ 16/23

SLIDE 17

The results of the dissertation publications

Publication II

10 20 30 0.5 1 10 20 30 0.5 1 10 20 30 0.5 1 Table index Improvement of the quality

f table-based BLIT

algorithms when the table is short Controllable window function Tabulated values as a result of an

ptimization problem

Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria, April 4, 2014 http://diss.pekonen.cc/ 17/23

SLIDE 18

The results of the dissertation publications

Publication III

−2 −1 1 2 0.2 0.4 0.6 Time (sample index) −2 −1 1 2 0.5 1 Time (sample index) Optimize the coefficients of the BLIT/BLEP polynomy Reduces aliasing even more than the polynomials discussed in Publication I Alias-free sawtooth waveform up to 12 kHz when the sample rate is 44.1 kHz

Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria, April 4, 2014 http://diss.pekonen.cc/ 18/23

SLIDE 19

The results of the dissertation publications

Publication IV

v1,1(n) ¯ H1,1(z) . . . . . . vN1,1(n) ¯ HN1,1(z) v1,2(n) ¯ H1,2(z) . . . . . . vN2,2(n) ¯ HN2,2(z) + Generate infinitely long BLIT/BLEP function Fixed feedback filters, delay-dependent burst triggers Attenuation of aliasing can be designed as an analog filter

Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria, April 4, 2014 http://diss.pekonen.cc/ 19/23

SLIDE 20

The results of the dissertation publications

Publication V

x(n)

1+p 2

+ z−1 p + y(n) − Reduce aliasing afterwards with filters x(n)

1 2

z−D Hfd(z) + y(n) x(n) 1 − c + c Hfd(z) z−D y(n)

Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria, April 4, 2014 http://diss.pekonen.cc/ 20/23

SLIDE 21

The results of the dissertation publications

Publication VI

2 4 6 8 10 12 14 16 18 20 22 24 26 Step of the listening test Subject 1 Subject 2 Audibility of aliasing in trivially generated sawtooth waveform at different fundamental frequencies The needed attenuation below and above the fundamental frequency Design criteria for oscillator algorithms based on the results

Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria, April 4, 2014 http://diss.pekonen.cc/ 21/23

SLIDE 22

The results of the dissertation publications

Publication VII

5 10 −1 1 0.5 1 −1 1 Time (ms) The oscillator circuit of an analog synthesizer produces slightly different waveforms Phase distortion and filter models of the sawtooth waveform of MiniMoog Voyager synthesizer

Source of the MiniMoog image: www.moogmusic.com/products/minimoog-voyagers/minimoog-voyager-old-school

Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria, April 4, 2014 http://diss.pekonen.cc/ 22/23

SLIDE 23

Summary

Improvements to quasi-bandlimited oscillator algorithms (Publications I-IV)

Generalization of polynomial-based BLEP algorithms (Publication I) and their optimization (Publication III) Improvement of the quality of table-based BLIT algorith with short table lengths (Publication II) Digital generation of infinitely long BLIT/BLEP functions (Publication IV)

Reduction of aliasing with post-processing filters (Publication V) Analysis of audibility of aliasing with a listening test (Publication VI) Modification of a digital oscillator to match better the waveform

f an analog synthesizer (Publication VII)

Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria, April 4, 2014 http://diss.pekonen.cc/ 23/23