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

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 oscillators and aliasing 2 Antialiasing oscillator algorithms 3 The results of the dissertation publications 4 Summary 5 Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria , April 4, 2014 http://diss.pekonen.cc/ 2/23

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

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

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

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

Sound example IV ”Overworld” theme from the game Super Mario Bros Composer: Koji Kondo In fact digital subtractive synthesis, only 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

Subtractive synthesis Source-filter synthesis Output Oscillator Filter 5 5 5 0 1 2 3 4 0 1 2 3 4 0 1 2 3 4 Frequency (kHz) Frequency (kHz) 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

Analog oscillator V + − V + − + V − + V − 1 1 1 0 0 0 − 1 − 1 − 1 0 2 T 0 0 2 T 0 0 2 T 0 T 0 T 0 T 0 Time (s) Time (s) Time (s) Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria , April 4, 2014 http://diss.pekonen.cc/ 9/23

Trivial digital oscillators − 1 2 p ( n ) + + s ( n ) f 0 T s mod1 1 z − 1 − 2 P s ( n ) + s t ( n ) abs sgn p ( n ) + r ( n ; P ) − Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria , April 4, 2014 http://diss.pekonen.cc/ 10/23

Aliasing in digital oscillators 0 Listen! (Without aliasing) Magnitude (dB) − 20 − 40 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 Frequency ( × sample rate) 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

Bandlimited algorithms 0 Magnitude (dB) − 20 − 40 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 Frequency ( × sample rate) Additive synthesis Discrete Summation Formulae Wavetable synthesis Inverse FFT synthesis Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria , April 4, 2014 http://diss.pekonen.cc/ 12/23

Quasi-bandlimited algorithms 0 Magnitude (dB) − 20 − 40 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 Frequency ( × sample rate) 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

Alias-suppressing algorithms 0 Magnitude (dB) − 20 − 40 0 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 Frequency ( × sample rate) Oversampled Differentiated polynomial waveform Filtered full-wave rectified sine Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria , April 4, 2014 http://diss.pekonen.cc/ 14/23

Ad-hoc algorithms The purpose is to produce signals 1 that resemble the classical waveforms, but not necessarily 0 without aliasing − 1 0 1 2 Time ( × T 0 ) 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

The results of the dissertation publications Publication I 1 1 0 . 5 0 . 5 0 0 − 2 − 1 0 1 2 − 2 − 1 0 1 2 1 1 0 . 5 0 . 5 0 0 − 2 − 1 0 1 2 − 2 − 1 0 1 2 1 1 0 . 5 0 . 5 0 0 − 2 − 1 0 1 2 − 2 − 1 0 1 2 Time (sample index) 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

The results of the dissertation publications Publication II Improvement of the quality 1 of table-based BLIT 0 . 5 algorithms when the table 0 is short 0 10 20 30 1 Controllable window 0 . 5 function 0 Tabulated values as a 0 10 20 30 result of an 1 optimization problem 0 . 5 0 0 10 20 30 Table index Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria , April 4, 2014 http://diss.pekonen.cc/ 17/23

The results of the dissertation publications Publication III 0 . 6 1 0 . 4 0 . 5 0 . 2 0 0 − 2 − 1 0 1 2 − 2 − 1 0 1 2 Time (sample index) 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

The results of the dissertation publications Publication IV Generate infinitely long ¯ v 1 , 1 ( n ) H 1 , 1 ( z ) BLIT/BLEP function . . Fixed feedback filters, . . . . delay-dependent burst triggers ¯ v N 1 , 1 ( n ) H N 1 , 1 ( z ) Attenuation of aliasing + can be designed as an v 1 , 2 ( n ) ¯ H 1 , 2 ( z ) analog filter . . . . . . v N 2 , 2 ( n ) ¯ H N 2 , 2 ( z ) Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria , April 4, 2014 http://diss.pekonen.cc/ 19/23

The results of the dissertation publications Publication V Reduce aliasing 1+ p 2 afterwards with x ( n ) + z − 1 + y ( n ) filters − p 1 2 x ( n ) z − D H fd ( z ) + y ( n ) 1 − c x ( n ) + y ( n ) c H fd ( z ) z − D Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen Lectio Praecursoria , April 4, 2014 http://diss.pekonen.cc/ 20/23

The results of the dissertation publications Publication VI Subject 1 Subject 2 2 4 6 8 10 12 14 16 18 20 22 24 26 Step of the listening test 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

The results of the dissertation publications Publication VII The oscillator circuit of an 1 analog synthesizer produces 0 slightly different waveforms Phase distortion and filter − 1 models of the sawtooth 0 5 10 waveform of MiniMoog 1 Voyager synthesizer 0 − 1 0 0 . 5 1 Time (ms) 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