DOCSLIB.ORG

Multicore, Multithreaded, Phase-Synchronous Fm Sound Synthesizer

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Multicore, Multithreaded, Phase-Synchronous Fm Sound Synthesizer MULTICORE, MULTITHREADED, PHASE-SYNCHRONOUS FM SOUND SYNTHESIZER by Justin Tomlin Senior Project ELECTRICAL ENGINEERING DEPARTMENT California Polytechnic State University San Luis Obispo 2011 1 Table of Contents List of Figures............................................................................................................................................ 3 Acknowledgements.................................................................................................................................... 4 Abstract...................................................................................................................................................... 5 Section 1 - Introduction..............................................................................................................................6 Project Overview/Motivation........................................................................................................... 6 Definition of Intended User.............................................................................................................. 6 Competitive Solutions...................................................................................................................... 6 Section 2 - Background..............................................................................................................................7 FM Synthesis.................................................................................................................................... 7 Common Parameter Modulation Schemes....................................................................................... 7 Section 3 - Requirements........................................................................................................................... 8 Functional Requirements.................................................................................................................. 8 Performance Specifications.............................................................................................................. 8 Section 4 - Design Approach Alternatives................................................................................................. 9 Oscillator...........................................................................................................................................9 Section 5 - Product Design.......................................................................................................................14 User Interface..................................................................................................................................14 Theory of Operation.................................................................................................................................15 Software Subsystems...................................................................................................................... 19 Software/Hardware Interfacing...................................................................................................... 22 Section 6 – Physical Construction and Integration.................................................................................. 23 Circuit Board Implementation........................................................................................................ 23 Enclosure Concept.......................................................................................................................... 23 Power Source.................................................................................................................................. 23 Section 7 – Integrated System Tests and Results..................................................................................... 25 Project (System-Level) Verification Testing...................................................................................25 Subsystem Verification Testing.......................................................................................................25 Summarized Test Results................................................................................................................31 Section 8 – Conclusions...........................................................................................................................32 Proposed Solutions to Design Shortcomings..................................................................................32 Further Improvements.................................................................................................................... 33 Section 9 – Bibliography..........................................................................................................................35 Appendix A: Parts List and Cost..............................................................................................................36 Budget.............................................................................................................................................36 Parts List:........................................................................................................................................ 36 Appendix B: Schedule.............................................................................................................................37 Appendix C: Program Listing.................................................................................................................. 39 Appendix D: Analysis of Senior Project Design.....................................................................................51 2 List of Figures Chapter 4 4.1: DPW Sawtooth Generation ........................................................................................ 9 4.2: tanh Square Generation............................................................................................... 10 4.3: tanh() function............................................................................................................. 10 4.4: Basic ModFM flowchart..............................................................................................11 4.5: Square to Triangle Conversion.................................................................................... 11 4.6: Phase-synchronous ModFM........................................................................................12 Chapter 5 5.1: Black Box Diagram..................................................................................................... 14 5.2: Photograph of Physical Interface.................................................................................15 5.3: Layout of Parameter Matrix........................................................................................ 15 5.4: Overall System Block Diagram...................................................................................16 5.5: Audio DAC Connection Diagram................................................................................17 5.6: ADC Connection Diagram...........................................................................................17 5.7: MIDI Interface Schematic........................................................................................... 18 5.8: Power Supply Schematic............................................................................................. 18 5.9: Software Subsystem Block Diagram...........................................................................19 5.10: I/O Port Map..............................................................................................................22 Chapter 6 6.1: Photograph of Board Implementation......................................................................... 23 6.2: Photograph of Panel Wiring........................................................................................ 24 Chapter 7 7.1: Power Supply/DAC Load Testing............................................................................... 25 7.2: AVDD Supply Noise....................................................................................................26 7.3: AVSS Supply Noise..................................................................................................... 26 7.4: Frequency Spectrum of 440 Hz Cosine Output...........................................................27 7.5: Frequency Spectrum (fo = 1760, k = 63, n = 7).......................................................... 28 7.6: Envelope Modulation of Amplitude (short and long attack/decay).............................28 7.7: Envelope Modulation of k (long attack, A440, n=2)...................................................29 7.8: LFO Modulation of Amplitude (short and long period).............................................. 29 7.9: LFO Modulation of k (long period, A440, n=2)..........................................................30 7.10: Plot for Determining Audio Latency......................................................................... 30 7.11: Performance Specification Test Results.................................................................... 31 3 Acknowledgements First of all, I would like to thank my senior project advisor Dr. Pilkington for his assistance in planning this project and addressing issues that came up along the way. The digital signal processing techniques and MATLAB exercises taught in his EE 419/459 lecture and lab were also invaluable in my research and design process. Secondly, I would like to thank Texas Instruments for fulfilling my multiple sample requests while
Load more

Recommended publications
  • Theory and Practice of Modified Frequency Modulation Synthesis*
    PAPERS Theory and Practice of Modified Frequency Modulation Synthesis* VICTOR LAZZARINI AND JOSEPH TIMONEY ([email protected]) ([email protected]) Sound and Music Technology Group, National University of Ireland, Maynooth, Ireland The theory and applications of a variant of the well-known synthesis method of frequency modulation, modified frequency modulation (ModFM), is discussed. The technique addresses some of the shortcomings of classic FM and provides a more smoothly evolving spectrum with respect to variations in the modulation index. A complete description of the method is provided, discussing its characteristics and practical considerations of instrument design. A phase synchronous version of ModFM is presented and its applications on resonant and formant synthesis are explored. Extensions to the technique are introduced, providing means of changing spectral envelope symmetry. Finally its applications as an adaptive effect are discussed. Sound examples for the various applications of the technique are offered online. 0 INTRODUCTION tion we will examine further applications in complement to the ones presented in [11]. We will also look at exten- The elegance and efficiency of closed-form formulas, sions to the basic technique as well as its use as an adap- which arise in various distortion synthesis algorithms, rep- tive effect. resent a resource for instrument design that is explored too rarely. Among the many techniques in this group there 1 SIMPLE MODFM SYNTHESIS are frequency modulation synthesis [1], summation formula method [2], nonlinear waveshaping [3], [4], and phase dis- ModFM synthesis represents an interesting alternative tortion [5]. Some of these techniques remain largely for- to the well-known FM [1] (or phase-modulation) synthe- gotten, even when many useful applications for them can sis.
    [Show full text]
  • Pdf Nord Modular
    Table of Contents 1 Introduction 1.1 The Purpose of this Document 1.2 Acknowledgements 2 Oscillator Waveform Modification 2.1 Sync 2.2 Frequency Modulation Techniques 2.3 Wave Shaping 2.4 Vector Synthesis 2.5 Wave Sequencing 2.6 Audio-Rate Crossfading 2.7 Wave Terrain Synthesis 2.8 VOSIM 2.9 FOF Synthesis 2.10 Granular Synthesis 3 Filter Techniques 3.1 Resonant Filters as Oscillators 3.2 Serial and Parallel Filter Techniques 3.3 Audio-Rate Filter Cutoff Modulation 3.4 Adding Analog Feel 3.5 Wet Filters 4 Noise Generation 4.1 White Noise 4.2 Brown Noise 4.3 Pink Noise 4.4 Pitched Noise 5 Percussion 5.1 Bass Drum Synthesis 5.2 Snare Drum Synthesis 5.3 Synthesis of Gongs, Bells and Cymbals 5.4 Synthesis of Hand Claps 6 Additive Synthesis 6.1 What is Additive Synthesis? 6.2 Resynthesis 6.3 Group Additive Synthesis 6.4 Morphing 6.5 Transients 6.7 Which Oscillator to Use 7 Physical Modeling 7.1 Introduction to Physical Modeling 7.2 The Karplus-Strong Algorithm 7.3 Tuning of Delay Lines 7.4 Delay Line Details 7.5 Physical Modeling with Digital Waveguides 7.6 String Modeling 7.7 Woodwind Modeling 7.8 Related Links 8 Speech Synthesis and Processing 8.1 Vocoder Techniques 8.2 Speech Synthesis 8.3 Pitch Tracking 9 Using the Logic Modules 9.1 Complex Logic Functions 9.2 Flipflops, Counters other Sequential Elements 9.3 Asynchronous Elements 9.4 Arpeggiation 10 Algorithmic Composition 10.1 Chaos and Fractal Music 10.2 Cellular Automata 10.3 Cooking Noodles 11 Reverb and Echo Effects 11.1 Synthetic Echo and Reverb 11.2 Short-Time Reverb 11.3 Low-Fidelity
    [Show full text]
  • 3. Performative Modulation
    %FQBSUNFOUPG4JHOBM1SPDFTTJOHBOE"DPVTUJDT " BM ,#ŗ U P % % & )(&#(,ŗ-.,.ŗ)/(ŗ #') & ŗ ) 3(."-#-ŗ&!),#."'-ŗ (& #( ,ŗ-. +BSJ,MFJNPMB , . ŗ) /(ŗ3(. " -#-ŗ& !) ,#. " '-ŗ 9HSTFMG*afabfh+ 9HSTFMG*afabfh+ *4#/ #64*/&44 *4#/ QEG &$0/0.: *44/- *44/ "35 *44/ QEG %&4*(/ "3$)*5&$563& " B "BMUP6OJWFSTJUZ M U 4DIPPMPG&MFDUSJDBM&OHJOFFSJOH 4$*&/$& P %FQBSUNFOUPG4JHOBM1SPDFTTJOHBOE"DPVTUJDT 5&$)/0-0(: 6 XXXBBMUPGJ OJ W $304407&3 F S T %0$503"- J %0$503"- U %*44&35"5*0/4 Z %*44&35"5*0/4 Aalto University publication series DOCTORAL DISSERTATIONS 25/2013 Nonlinear Abstract Sound Synthesis Algorithms Jari Kleimola A doctoral dissertation completed for the degree of Doctor of Science in Technology to be defended, with the permission of the Aalto University School of Electrical Engineering, at a public examination held at the lecture hall S1 of the school on 22 February 2013 at 12 noon. Aalto University School of Electrical Engineering Department of Signal Processing and Acoustics Supervising professor Prof. Vesa Välimäki Thesis advisor Prof. Vesa Välimäki Preliminary examiners Dr. Tamara Smyth, Simon Fraser University Surrey, Canada Prof. Roger B. Dannenberg, Carnegie Mellon University, USA Opponent Prof. Philippe Depalle, McGill University, Canada Aalto University publication series DOCTORAL DISSERTATIONS 25/2013 © Jari Kleimola ISBN 978-952-60-5015-7 (printed) ISBN 978-952-60-5016-4 (pdf) ISSN-L 1799-4934 ISSN 1799-4934 (printed) ISSN 1799-4942 (pdf) http://urn.fi/URN:ISBN:978-952-60-5016-4 Unigrafia Oy Helsinki 2013 Finland Abstract
    [Show full text]
  • Kivonó Színtézis) – Analóg Szintézis
    Széchenyi István Egyetem Műszaki Tudományi Kar DIPLOMAMUNKA Laczkovits Áron Villamosmérnöki MSc szak 2013 SZÉCHENYI ISTVÁN EGYETEM MŰSZAKI TUDOMÁNYI KAR Távközlési Tanszék DIPLOMAMUNKA Hangszíntézisek Laczkovits Áron Villamosmérnöki MSc szak Távközlési rendszerek és szolgáltatások szakirány Győr, 2013 Feladatkiírás Diplomamunka címe: Hangszíntézis módszerek Hallgató neve: Laczkovits Áron Szak: Villamosmérnöki Képzési szint: MSc Típus: nyilvános A diplomaterv keretében a meglévő szintézis módszerek csoportosítását, bemutatását, valamint e módszerek objektív összehasonlítását kell elvégezni. Minden csoportba reprezentatív hang színtézis technikákat választva. A kiválasztott színtézis módszerek a hozzájuk szorosan kapcsolódó szempontok szerint kerüljenek osztályozásra. Mutassa be a hang és szintéziseinek elméleti alapjait. Ismertesse a különböző hangszintézis csoportokat. Valósítsa meg a kiválasztott hangszintéziseket MATLAB programmal. Vizsgálja meg a szintézisek hatásfokát a paraméterek változtatásával. A számítási kapacitások és a hatásfok eredmények alapján határozza meg az optimális a paraméterek értékeit. Értékelje a kapott eredményeket és hasonlítsa össze különböző szintéziseket. Győr, 2013-02-18 ______________________ ______________________ belső konzulens tanszékvezető Értékelő lap Diplomamunka címe: Hangszíntézis módszerek Hallgató neve: Laczkovits Áron Szak: Villamosmérnöki Képzési szint: MSc Típus: nyilvános A diplomamunka beadható / nem adható be: (a nem kívánt rész törlendő) ____________________ _____________________ dátum
    [Show full text]
  • Fabián Esqueda Native Instruments Gmbh 1.3.2019
    SOUND SYNTHESIS FABIÁN ESQUEDA NATIVE INSTRUMENTS GMBH 1.3.2019 © 2003 – 2019 VESA VÄLIMÄKI AND FABIÁN ESQUEDA SOUND SYNTHESIS 1.3.2019 OUTLINE ‣ Introduction ‣ Introduction to Synthesis ‣ Additive Synthesis ‣ Subtractive Synthesis ‣ Wavetable Synthesis ‣ FM and Phase Distortion Synthesis ‣ Synthesis, Synthesis, Synthesis SOUND SYNTHESIS 1.3.2019 Introduction ‣ BEng in Electronic Engineering with Music Technology Systems (2012) from University of York. ‣ MSc in Acoustics and Music Technology in (2013) from University of Edinburgh. ‣ DSc in Acoustics and Audio Signal Processing in (2017) from Aalto University. ‣ Thesis topic: Aliasing reduction in nonlinear processing. ‣ Published on a variety of topics, including audio effects, circuit modeling and sound synthesis. ‣ My current role is at Native Instruments where I work as a Software Developer for our Synths & FX team. ABOUT NI SOUND SYNTHESIS 1.3.2019 About Native Instruments ‣ One of largest music technology companies in Europe. ‣ Founded in 1996. ‣ Headquarters in Berlin, offices in Los Angeles, London, Tokyo, Shenzhen and Paris. ‣ Team of ~600 people (~400 in Berlin), including ~100 developers. SOUND SYNTHESIS 1.3.2019 About Native Instruments - History ‣ First product was Generator – a software modular synthesizer. ‣ Generator became Reaktor, NI’s modular synthesis/processing environment and one of its core products to this day. ‣ The Pro-Five and B4 were NI’s first analog modeling synthesizers. SOUND SYNTHESIS 1.3.2019 About Native Instruments ‣ Pioneered software instruments and digital
    [Show full text]
  • Analog Violin Audio Synthesizer
    ANALOG VIOLIN AUDIO SYNTHESIZER by Brandon Davis Senior Project ELECTRICAL ENGINEERING DEPARTMENT California Polytechnic State University San Luis Obispo 2014 TABLE OF CONTENTS Section Page List of Tables and Figures………………………………………………………………………………3 Acknowledgements……………………………………………………………………………………..7 Abstract…………………………………………………………………………………………………8 1. Introduction…………………………………………………………………………………………..9 2. Background…………………………………………………………………......................................10 3. Requirements and Specifications………………...………………………………………………….10 4. Design Approach Alternatives……………………………………………………………...………..12 5. Project Design………………………………………………………………………………………...13 5.1 Level 0 Functional Decomposition………………………………………………………...13 5.2 Level 1 Functional Decomposition………………………………………………………...14 5.3 Level 2 Functional Decomposition………………………………………………………...15 5.3.1 Touch Sensor…………………………………………………………………….15 5.3.2 Oscillator 1 and Oscillator 2……………………………………………………..17 5.3.3 Low Frequency Oscillator (LFO)………………………………………………..20 5.3.4 Mixer ……………………………………………………………………………22 5.3.5 Envelope Generator Circuits…………………………………………………….23 5.3.5.1 Amplifier Envelope Generator………………………………………..25 5.3.5.2 Low-Pass Filter Envelope Generator…………………………………26 5.3.5.3 Envelope Buffer Stage………………………………………………...28 5.3.6 Voltage-Controlled Amplifier (VCA)…………………………………………...28 5.3.7 Voltage-Controlled (Low-Pass) Filter…………………………………………..30 5.3.8 Output Stage……………………………………………………………………..32 5.3.9 Power Supply…………………………………………………………………….32 6. Physical Construction and Integration……………………………………………………………….34
    [Show full text]
  • Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Aalto University
    Department of Signal Processing and Acoustics Aalto- Jussi Pekonen Pekonen Jussi Digital modeling of the subtractive sound synthesis principle used in analog DD 26 Filter-Based Oscillator synthesizers has been a popular research / topic in the past few years. In subtractive 2014 sound synthesis, a spectrally rich oscillator Algorithms for Virtual signal is filtered with a time-varying filters. Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Synthesis Analog Virtual for Algorithms Oscillator Filter-Based The trivial digital implementation of the oscillator waveforms typically used in this Analog Synthesis synthesis method suffers from disturbing aliasing distortion. This thesis presents efficient filter-based algorithms that produce these waveforms with reduced Jussi Pekonen aliasing. In addition, perceptual aspects of audibility of aliasing and modeling of analog synthesizer oscillator output signals are addressed. V+ V+ − + − V + − V − 9HSTFMG*affiig+ ISBN 978-952-60-5588-6 BUSINESS + ISBN 978-952-60-5586-2 (pdf) ECONOMY ISSN-L 1799-4934 ISSN 1799-4934 ART + ISSN 1799-4942 (pdf) DESIGN + ARCHITECTURE University Aalto Aalto University School of Electrical Engineering SCIENCE + Department of Signal Processing and Acoustics TECHNOLOGY www.aalto.fi CROSSOVER DOCTORAL DOCTORAL DISSERTATIONS DISSERTATIONS Aalto University publication series DOCTORAL DISSERTATIONS 26/2014 Filter-Based Oscillator Algorithms for Virtual Analog Synthesis Jussi Pekonen A doctoral dissertation completed for the degree of Doctor of Science (Technology) to be defended, with the permission of the Aalto University School of Electrical Engineering, at a public examination held at the lecture hall S1 of the school on 4 April 2014 at 12. Aalto University School of Electrical Engineering Department of Signal Processing and Acoustics Supervising professor Prof.
    [Show full text]
  • FREQUENCY MODULATION (FM) SYNTHESIS + Phase Distortion (PD) Frequency Modulation (FM)
    Electronic musical instruments FREQUENCY MODULATION (FM) SYNTHESIS + phase distortion (PD) Frequency modulation (FM) FM – frequency modulation, used since 1920s to transmit radio waves: • transmitted signal (modulator) – e.g. radio broadcast • carrier signal – high frequency sine (e.g. 99.8 MHz) • amplitude of the transmitted signal modulates instantaneous frequency of the carrier • modulated signal is transmitted on air • the received signal is demodulated • we obtain the original signal source: http://slidedeck.io/jsantell/dsp-with-web-audio-presentation FM in sound synthesis 1973 – John Chowning published a paper: „The Synthesis of Complex Audio Spectra by Means of Frequency Modulation”. • If the two signals have specific frequencies, a harmonic signal is obtained. • Changes in modulator amplitude modify the timbre. • Multiple modulations may be performed. • Easy and cheap method of digital sound synthesis. • Patented in 1975-1995 by Chowning and Yamaha. FM in sound synthesis Let’s simplify the problem to two sine oscillators: • carrier signal (C) xc(t) = A sin(t) • modulating signal (M) xm(t) = I sin(t) The modulator changes (modulates) the instantaneous frequency of the carrier signal: x(t) = A sin[t + xm(t)] x(t) = A sin[t + I sin(t)] Frequency modulation in sound What effect does FM produce? • Low modulating frequency (<1 Hz): slow wobbling of the pitch (just like LFO in the subtractive synthesis). • Modulating frequency in 1 Hz – 20 Hz range: an increasing vibrato effect. • Frequency above 20 Hz: an inharmonic sound is produced,
    [Show full text]
  • Vector Phaseshaping Synthesis
    Proc. of the 14th Int. Conference on Digital Audio Effects (DAFx-11), Paris, France, September 19-23, 2011 VECTOR PHASESHAPING SYNTHESIS Jari Kleimola*, Victor Lazzariniy, Joseph Timoneyy, Vesa Välimäki* *Aalto University School of Electrical Engineering Espoo, Finland yNational University of Ireland, Maynooth Ireland [email protected], [email protected], [email protected] [email protected] ABSTRACT aliasing, whose application will be explored later in this paper. Fi- nally, waveshaping, as it is based on a non-linear amplification This paper introduces the Vector Phaseshaping (VPS) synthesis effect, almost always requires care in terms of gain scaling to be technique, which extends the classic Phase Distortion method by usable. This is not, in general, a requirement for phaseshaping. providing a flexible method to distort the phase of a sinusoidal os- After a brief introduction to the original PD synthesis tech- cillator. This is done by describing the phase distortion function nique, this paper is organized as follows. Section 3 introduces the using one or more breakpoint vectors, which are then manipulated VPS method by defining the multi-point vectorial extension, deriv- in two dimensions to produce waveshape modulation at control ing its spectral description, and proposing a novel alias-suppression and audio rates. The synthesis parameters and their effects are method. Section 4 explores control rate modulation of the vector explained, and the spectral description of the method is derived. in 1-D, 2-D and multivector configurations, while Section 5 com- Certain synthesis parameter combinations result in audible alias- plements this at audio rates. Finally, Section 6 concludes.
    [Show full text]
  • Digital Emulation of Distortion Effects by Wave and Phase Shaping Methods
    Proc. of the 13th Int. Conference on Digital Audio Effects (DAFx-10), Graz, Austria, September 6-10, 2010 DIGITAL EMULATION OF DISTORTION EFFECTS BY WAVE AND PHASE SHAPING METHODS Joseph Timoney†, Victor Lazzarini†, Anthony Gibney† and Jussi Pekonen †† †Sound and Music Technology Group ††Dept. Signal Processing and Acoustics National University of Ireland Aalto University School of Science and Technology Maynooth, Ireland Espoo, Finland [email protected], [email protected] [email protected] ABSTRACT music production environment. Emulation using the algorithmic approach can be divided into a nonlinear system model with This paper will consider wave and phase signal shaping tech- memory or without memory [9]. However, incorporating mem- niques for the digital emulation of distortion effect processing. ory for systems with strong nonlinearities is computationally ex- We examine in detail how to determine the wave and phase shap- pensive for real-time synthesis [10]. Thus, it is more common to ing functions with harmonic amplitude data only first, and then use a nonlinear system that is memoryless. after including the harmonic phase data. Three distortion effects The action of such a nonlinear system is understood as wave- units are used to provide test data. Wave and phase shaping func- shaping [11], a form of amplitude distortion. It has been shown tions for the emulation of these effects are derived with the assis- more recently that distortion can also be applied to the signal tance of a super-resolution frequency-domain analysis technique. phase to achieve a similar result [12], [13], [14], although no In complement to this, we describe an alternative time domain complete theory for this is available.
    [Show full text]
  • 6 Chapter 6 MIDI and Sound Synthesis
    6 Chapter 6 MIDI and Sound Synthesis ................................................ 2 6.1 Concepts .................................................................................. 2 6.1.1 The Beginnings of Sound Synthesis ........................................ 2 6.1.2 MIDI Components ................................................................ 4 6.1.3 MIDI Data Compared to Digital Audio ..................................... 7 6.1.4 Channels, Tracks, and Patches in MIDI Sequencers ................ 11 6.1.5 A Closer Look at MIDI Messages .......................................... 14 6.1.5.1 Binary, Decimal, and Hexadecimal Numbers .................... 14 6.1.5.2 MIDI Messages, Types, and Formats ............................... 15 6.1.6 Synthesizers vs. Samplers .................................................. 17 6.1.7 Synthesis Methods ............................................................. 19 6.1.8 Synthesizer Components .................................................... 21 6.1.8.1 Presets ....................................................................... 21 6.1.8.2 Sound Generator .......................................................... 21 6.1.8.3 Filters ......................................................................... 22 6.1.8.4 Signal Amplifier ............................................................ 23 6.1.8.5 Modulation .................................................................. 24 6.1.8.6 LFO ............................................................................ 24 6.1.8.7 Envelopes
    [Show full text]
  • Phaseshaping Oscillator Algorithms for Musical Sound Synthesis
    PHASESHAPING OSCILLATOR ALGORITHMS FOR MUSICAL SOUND SYNTHESIS Jari Kleimola 1, Victor Lazzarini 2, Joseph Timoney 2, and Vesa Välimäki 1 1 Department of Signal Processing and Acoustics, Aalto University, Espoo, Finland 2 Sound and Digital Music Technology Group, National University of Ireland, Maynooth, Ireland [email protected],[email protected],[email protected],[email protected] ABSTRACT where f[.] is an arbitrary nonlinear function called a wa- veshaper . The well-known classic FM synthesis equation, This paper focuses on phaseshaping techniques and their for instance, can be rewritten as a waveshaping expres- relation to classical abstract synthesis methods. Elemen- sion tary polynomial and geometric phaseshapers, such as those based on the modulo operation and linear transfor- cos [ω n + xI (n)] = c (3) ω [][]− ω mations, are investigated. They are then applied to the cos( c n)cos xI (n) sin( c n)sin xI (n) , generation of classic and novel oscillator effects by using ω nested phaseshaping compositions. New oscillator algo- where c is the carrier frequency and the waveshapers rithms introduced in this paper include single-oscillator cos(.) and sin(.) act on the sinusoidal modulation signal hard sync, triangle modulation, efficient supersaw simu- x(n) of Equation 1. lation, and sinusoidal waveshape modulation effects. The Similarly, it is possible to describe PD as a form of digital waveforms produced with phaseshaping tech- waveshaping. This is demonstrated by starting with the following expression defining a sinusoidal oscillator: niques are generally discontinuous, which leads to alias- = [ πφ ] ing artifacts. Aliasing can be effectively reduced by mod- y(n) cos 2 (n .) (4) ifying samples around each discontinuity using the pre- viously proposed polynomial bandlimited step function The function φ(n) is the normalized phase defined by (polyBLEP) method.
    [Show full text]