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Real-Time Signal Processing on Field Programmable Gate Array Hardware

  • Chapter
Springer Handbook of Systematic Musicology

Part of the book series: Springer Handbooks ((SHB))

Abstract

Over the last 50 years, advances in high-speed digital signal processing (GlossaryTerm

DSP

) and numerical methods for audio signal processing in general were fueled by the rising processing capabilities of personal computers (GlossaryTerm

PC

s). Added to this was the advent of specialized coprocessing platforms like general purpose graphics processing units (GlossaryTerm

GPGPU

s), central processing unit (GlossaryTerm

CPU

)-based accelerators like Intel's Xeon Phi platforms as well as high-performance digital signal processing (GlossaryTerm

DSP

) chips like Analog Devices' TigerSHARC. Still, there are applications that are not realizable on the mentioned devices in real time or even close to real time. This chapter gives an introduction to field programmable gate array (GlossaryTerm

FPGA

) hardware, a flexible computing platform with massively parallel logic capability that is applicable for problems of high data throughput, high clock rates and high parallelism. After an introduction to the basic structure of FPGAs, several features that enable high-throughput DSP applications are highlighted. An introduction to development platforms as well as the development methodology is given, along with an overview of current FPGA devices and their specific capabilities. Two application examples and an outlook and summary complete this chapter.

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Abbreviations

1-D:

one-dimensional

1C:

one's complement

2-D:

two-dimensional

2C:

two's complement

3-D:

three-dimensional

ADC:

analog-to-digital converter

ALM:

adaptive logic module

ASIC:

application-specific integrated circuit

ASSP:

application-specific standard part

BC:

boundary condition

BLAS:

basic linear algebra subprograms

BRAM:

block RAM

CAD:

computer-aided design

CFL:

Courant–Friedrichs–Levy

CLB:

configurable logic block

codec:

coder-decoder

CPU:

central processing unit

DAC:

digital-to-analog converter

DDR:

double data rate

DIY:

do-it-yourself

DSP:

digital signal processing

EEPROM:

electrically erasable programmable read-only memory

EPROM:

erasable programmable read-only memory

FD:

finite difference

FDTD:

finite-difference time domain

FFT:

fast Fourier transform

FFTW:

fastest Fourier transform in the West

FIFO:

first in/first out

FIR:

finite impulse response

FMC:

FPGA mezzanine card

FPGA:

field programmable gate array

FSM:

finite-state machine

GPGPU:

general purpose graphics processing unit

GUI:

graphical user interface

HDL:

hardware description language

HLS:

high-level synthesis

HPC:

high-performance computing

I/O:

input/output

I2S:

inter-IC sound

IIR:

infinite impulse response

IL:

interface layer

IP:

intellectual property

LTI:

linear time-invariant

LUT:

look-up table

MAC:

multiply-and-accumulate

MoR:

model routing layer

NTT:

number theoretic transform

PCIe:

peripheral component interconnect express

PCM:

pulse code modulation

PC:

personal computer

PDE:

partial differential equation

PLD:

programmable logic device

PROMS:

programmable read-only memory

RAM:

random access memory

RSV:

reserved

RTL:

register transfer level

SATA:

serial advanced technology attachment

SPI:

serial peripheral interface

TFLOPS:

tera floating point operations per second

TMACS:

tera multiply-and-accumulates per second

ucf:

user constraint file

USB:

universal serial bus

VHDL:

very high speed integrated circuit hardware description language

WDF:

wave digital filter

References

  1. Cisco: Cisco Visual Networking Index: Global Mobile Data Traffic Forecast Update, 2015–2020 White Paper (Cisco Systems Inc., San Jose 2016)

    Google Scholar 

  2. A. Brandt: Noise and Vibration Analysis: Signal Analysis and Experimental Procedures (Wiley, Chichester 2011)

    Book  Google Scholar 

  3. E.S. Gopi: Digital Signal Processing for Medical Imaging Using MATLAB (Springer, New York 2013)

    Book  Google Scholar 

  4. U. Zölzer, X. Amatriain, D. Arfib, J. Bonada, G. De Poli, P. Dutilleux, G. Evangelista, F. Keiler, A. Loscos, D. Rocchesso, M. Sandler, X. Serra, T. Todoroff: DAFX: Digital Audio Effects (Wiley, Chichester 2002)

    Google Scholar 

  5. M. Holters, U. Zölzer: Physical modelling of a wah-wah effect pedal as a case study for application of of the nodal DK method to circuits with variable parts. In: Proc. 14th Int. Conf. Digit. Audio Eff. DAFx-11 (2011) pp. 31–35

    Google Scholar 

  6. D. Arfib: Different ways to write digital audio effects programs. In: Proc. Digit. Audio Eff. (DAFx-98), Barcelona (1998) pp. 188–191

    Google Scholar 

  7. K. Zuse: Der Computer - Mein Lebenswerk (Springer, Berlin, Heidelberg 2010)

    Book  Google Scholar 

  8. J. Fowers, G. Brown, P. Cooke, G. Stitt: A performance and energy comparison of FPGAs, GPUs, and multicores for sliding-window applications. In: Proc. ACM/SIGDA Int. Symp. Field Prog. Gate Arrays (ACM, New York 2012) pp. 47–56

    Google Scholar 

  9. G.W. Leibnitz: Explication de lárithmétique binaire, Mem. Acad. R. Sci. 3, 85–93 (1703)

    Google Scholar 

  10. F. Perkins: Leibniz and China: A Commerce of Light (Cambridge Univ. Press, Cambridge 2009)

    Google Scholar 

  11. G. Boole: The Mathematical Analysis of Logic (Philosophical Library, New York 1847)

    MATH  Google Scholar 

  12. G. Boole: An Investigation of the Laws of Thought: On Which are Founded the Mathematical Theories of Logic and Probabilities (Dover, Mineola 1854)

    MATH  Google Scholar 

  13. T. Hailperin: Boole’s algebra isn’t Boolean algebra, Math. Mag. 54(4), 173 (1981)

    Article  MathSciNet  Google Scholar 

  14. J. Corcoran: Aristotle’s prior analytics and Boole’s laws of thought, Hist. Phil. Log. 24(4), 261–288 (2003)

    Article  MathSciNet  Google Scholar 

  15. C.E. Shannon: A Symbolic Analysis of Relay and Switching Circuits, Ph.D. Thesis (Massachusetts Insitute of Technology, Cambridge 1940)

    Google Scholar 

  16. B.J. Copeland (Ed.): Colossus: The Secrets of Bletchley Park’s Codebreaking Computers (Oxford Univ. Press, Oxford 2006)

    Google Scholar 

  17. P.E. Ceruzzi: Computing: A Concise History, The MIT Press Essential Knowledge Series (MIT Press, Cambridge 2012)

    Google Scholar 

  18. C. Maxfield: The Design Warriors Guide to FPGAs (Elsevier, Oxford 2004)

    Google Scholar 

  19. L. Wirbel: Remembering Ross Freeman, http://www.edn.com/electronics-blogs/fpga-gurus/4306558/Remembering-Ross-Freeman (EDN Network 2009)

  20. L. Pantaleone, E. Todorivich: Accelerating embedded software processing in a FPGA with PowerPC and Microblaze. In: Natl. Conf. Inform. Eng. Inf. Syst., San Louis (2013)

    Google Scholar 

  21. N. Hemsoth: FPGAs Glimmer on the HPC Horizon, Glint in Hyperscale Sun, https://www.nextplatform.com/2015/11/17/fpgas-glimmer-on-the-hpc-horizon-glint-in-hyperscale-sun/ (The Next Platform 2015)

  22. T.P. Morgan: Why Hyperscalers And Clouds Are Pushing Intel Into FPGAs, https://www.nextplatform.com/2015/07/29/why-hyperscalers-and-clouds-are-pushing-intel-into-fpgas/ (The Next Platform 2015)

  23. Xilinx: Configurable Logic Block User Guide (Xilinx, San Jose 2010)

    Google Scholar 

  24. Xilinx: Virtex-6 FPGA Configurable Logic Block User Guide (Xilinx, San Jose 2012)

    Google Scholar 

  25. Altera: Stratix V Device Handbook (Altera, San Jose 2015)

    Google Scholar 

  26. D.S. Brown, G.Z. Vranesic: Fundamentals of Digital Logic with VHDL Design, McGraw-Hill Series in Electrical and Computer Engineering, 3rd edn. (McGraw-Hill, New York 2009)

    Google Scholar 

  27. A.V. Pedroni: Circuit Design with VHDL (MIT Press, Cambridge 2004)

    Google Scholar 

  28. J. Reichardt, B. Schwarz: VHDL-Synthese: Entwurf digitaler Schaltungen und Systeme, 4th edn. (Oldenbourg, München 2009)

    Book  Google Scholar 

  29. J.P. Ashenden: The Designer’s Guide to VHDL, 3rd edn. (Morgan Kaufmann, San Francisco 2010)

    Google Scholar 

  30. P. Pong: FPGA Prototyping by VHDL Examples (Wiley-Interscience, Hoboken 2008)

    Google Scholar 

  31. M. Zwoliński: Digital System Design with VHDL, 2nd edn. (Prentice Hall, Harlow 2004)

    Google Scholar 

  32. J.P. Ashenden: The Designer’s Guide to VHDL, 2nd edn. (Morgan Kaufmann, San Francisco 2002)

    Google Scholar 

  33. A.H. Wilen, J.P. Schade, R. Thornburg: Introduction to PCI Express: A Hardware and Software Developer’s Guide, Engineer to Engineer Series (Intel, Santa Clara 2003)

    Google Scholar 

  34. C. McGinnis: PCI-SIG® Fast Tracks Evolution to 32GT/s with PCI Express 5.0 Architecture, http://www.businesswire.com/news/home/20170607005351/en/PCI-SIG%C2%AE-Fast-Tracks-Evolution-32GTs-PCI-Express (PCI-SIG 2017)

  35. H. Liebig, T. Flik, M. Menge: Mikroprozessortechnik und Rechnerstrukturen (Springer, London 2005)

    Google Scholar 

  36. C.M. Herbordt, T. VanCourt, Y. Gu, B. Sukhwani, A. Conti, J. Model, D. DiSabello: Achieving high performance with FPGA-based computing, Computer 40, 50–57 (2007)

    Article  Google Scholar 

  37. U.M. Baese: Digital Signal Processing with Field Programmable Gate Arrays, 2nd edn. (Springer, Berlin, Heidelberg 2007)

    MATH  Google Scholar 

  38. R. Woods (Ed.): FPGA-Based Implementation of Signal Processing Systems (Wiley, Chichester 2008)

    Google Scholar 

  39. B.A. Kahng, J. Lienig, L.I. Markov, J. Hu: VLSI Physical Design: From Graph Partitioning to Timing Closure (Springer, Dordrecht 2011)

    Book  Google Scholar 

  40. K. Veggeberg, A. Zheng: Real-time noise source identification using programmable gate array FPGA technology, Proc. Meet. Acoust. 5, 2582 (2009)

    Google Scholar 

  41. C. Hai, W. Ping: The high speed implementation of direction-of-arrival estimation algorithm, IEEE Int. Conf. Commun. Circuits Syst. West Sino Expo. 2, 922–925 (2002)

    Google Scholar 

  42. P. Chen, X. Tian, Y. Chen, X. Yang: Delay-sum beamforming on FPGA. In: ICSP 2008 Proc. (2008) pp. 2542–2545

    Google Scholar 

  43. A. Madanayake, L. Bruton, F. Comis, C. Comis: FPGA architectures for real-time 2D/3D FIR/IIR plane wave filters. In: Proc. Int. Symp. Circuits Syst. ISCAS, Vol. 3 (2004)

    Google Scholar 

  44. S. Kai, Y. Xu, S. Jiang, H. Zhu: Converting analog controllers to digital controllers with FPGA. In: 9th Int. Conf. Signal Process. (2008)

    Google Scholar 

  45. O. Maslennikow, A. Sergiyenko: Mapping DSP algorithms into FPGA. In: Int. Symp. Parallel Comput. Electr. Eng. (PARELEC'06), Bialystok (2006) pp. 208–213, https://doi.org/10.1109/PARELEC.2006.51

    Chapter  Google Scholar 

  46. T. Brich, K. Novacek, A. Khateb: The digital signal processing using FPGA. In: ISSE 2006, 29th Int. Spring Semin. Electron. Technol. (2006) pp. 322–324

    Chapter  Google Scholar 

  47. M. Liu, W. Kuehn, Z. Lu, A. Jantsch: System-on-an-FPGA design for real-time particle track recognition in physics experiments. In: 11th Euromicro Conf. Digit. Syst. Design Archit., Methods Tools (2008)

    Google Scholar 

  48. B. von Herzen: Signal processing at 250 mHz using high-performance FPGA’s, IEEE Trans. Very Large Scale Int. (VLSI) Syst. 6(2), 238–246 (1998)

    Article  Google Scholar 

  49. Z. Wang, R. Jin, J. Geng, Y. Fan: FPGA implementation of downlink DBF calibration. In: Antennas Propag. Soc. Int. Symp. (2005)

    Google Scholar 

  50. K.H. Moustafa, M.F. Ahmed, M. Romeh, A. Fahmy: Real time processing of a lattice wave digital matched filter. In: IEEE Int. Symp. Signal Process. Inf. Techol. ISSPIT (2011) pp. 404–408

    Google Scholar 

  51. S. Thilagam, P. Karthigaikumar: Implementation of adaptive noise canceller using FPGA for real-time applications. In: 2015 2nd Int. Conf. Electr. Commun. Syst. (ICECS), Coimbatore (2015) pp. 1711–1714, https://doi.org/10.1109/ECS.2015.7124878

    Chapter  Google Scholar 

  52. H.P. Afshar, P. Ienne: Highly versatile DSP blocks for improved FPGA arithmetic performance. In: Proc. IEEE Symp. Field-Prog. Custom Comput. Mach. FCCM (2010) pp. 29–236

    Google Scholar 

  53. L. Struyf, S. De Beugher, D.H. Van Uytsel, F. Kanters, T. Goedemé: The battle of the giants: A case study of GPU vs FPGA optimisation for real-time image processing, Proc. PECCS 1, 112–119 (2014)

    Google Scholar 

  54. W. Chen, P. Kosmas, M. Leeser, C. Rappaport: An FPGA implementation of the two-dimensional finite-difference time-domain (FDTD) algorithm. In: Proc. 2004 (ACM/SIGDA) 12th Int. Symp. Field Prog. Gate Arrays, New York (2004) pp. 213–222

    Google Scholar 

  55. J.A. Gibbons, D.M. Howard, A.M. Tyrrell: FPGA implementation of 1d wave equation for real-time audio synthesis, IEEE Proc. Comput. Digit. Tech. 152(5), 619–631 (2005)

    Article  Google Scholar 

  56. E. Motuk, R. Woods, S. Bilbao: Implementation of finite-differece schemes for the wave equation on FPGA. In: IEEE Int. Acoust. Speech Signal Process. ICASSP (2005) p. 3

    Google Scholar 

  57. E. Motuk, R. Woods, S. Bilbao, J. McAllistere: Design methodology for real-time FPGA-based sound synthesis, IEEE Trans. Signal Process. 55(12), 5833–5845 (2007)

    Article  MathSciNet  Google Scholar 

  58. H.E. Motuk: System-On-Chip Implementation of Real-Time Finite Difference Based Sound Synthesis, Ph.D. Thesis (Queen’s Univ., Belfast 2006)

    Google Scholar 

  59. G. Martins, M. Barata, L. Gomes: Low cost method to reproduce sound with FPGA. In: IEEE Int. Symp. Ind. Electron. ISIE (2008)

    Google Scholar 

  60. F. Pfeifle, R. Bader: Real-time finite difference physical models of musical instruments on a field programmable gate array (fpga). In: Proc. Int. Conf. Digit. Audio Eff. (DAFx-12), New York (2012) pp. 63–70

    Google Scholar 

  61. F. Pfeifle, R. Bader: Real-time finite difference method physical modeling of musical instruments using field-programmable gate array hardware, J. Audio Eng. Soc. 63(12), 1001–1016 (2015)

    Article  Google Scholar 

  62. K. Kroschel, K.-D. Kammeyer: Digitale Signalverarbeitung – Filterung und Spektralanalyse mit MATLAB-Übungen, 6th edn. (Vieweg+Teubner, Wiesbaden 2006)

    MATH  Google Scholar 

  63. N.T. Rajapaksha, C. Wijenayake, A. Madanayake, L.T. Bruton: Raster-scanned wave-digital filter architectures for multi-beam 2d IIR broadband beamforming. In: Proc. Int. Conf. Microelectron. ICM (2010) pp. 112–115

    Google Scholar 

  64. H. Li, A. Kummert, S. Schauland, J. Velten: 3D wave digital filter implementation on a virtex2 FPGA board with external SDRAM. In: 2009 Int. Workshop Multidimens. (nD) Syst., Thessaloniki (2009) pp. 1–5, https://doi.org/10.1109/NDS.2009.5191463

    Chapter  Google Scholar 

  65. S. Bilbao: Numerical Sound Synthesis: Finite Difference Schemes and Simulation in Musical Acoustics (Wiley, Chichester 2009)

    Book  Google Scholar 

  66. F. Pfeifle, R. Bader: Musical Acoustics, Neurocognition and Psychology of Music, Chapter Real-Time Physical Modelling of a Real Banjo Geometry Using FPGA Hardware Technology (Rolf Bader, Frankfurt am Main 2009) pp. 71–86

    Google Scholar 

  67. F. Pfeifle, R. Bader: Real-time virtual banjo model and measurements using a microphone array, J. Acoust. Soc. Am. 125(4), 2515–2515 (2009)

    Article  Google Scholar 

  68. F. Pfeifle, R. Bader: Membrane modes and air resonances of the banjo using physical modeling and microphone array measurements, J. Acoust. Soc. Am. 127(3), 1870–1870 (2010)

    Article  Google Scholar 

  69. S. Bilbao: Robust physical modeling sound synthesis for nonlinear systems, IEEE Signal Process. Mag. 24(2), 32–41 (2007)

    Article  Google Scholar 

  70. C. Jordan: Calculus of Finite Differences (Chelsea, New York 1950)

    MATH  Google Scholar 

  71. J. Strikwerda: Finite Difference Schemes and Partial Differential Equations, 2nd edn. (SIAM, Philadelphia 2005)

    MATH  Google Scholar 

  72. E. Hairer, C. Lubich, G. Wanner: Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations, Springer Series in Computational Mathematics, Vol. 31 (Springer, Berlin, Heidelberg 2002)

    MATH  Google Scholar 

  73. R. Bader: Computational Mechanics of the Classical Guitar (Springer, Berlin, Heidelberg 2005)

    Google Scholar 

  74. R. Bader: Nonlinearities in the sound production of the classical guitar. In: Proc. Forum Acust. 2005 (2005) pp. 685–689

    Google Scholar 

  75. B.E. Moore: Conformal multi-symplectic integration methods for forced-damped semi-linear wave equations, Math. Comput. Simul. 80(1), 20–28 (2009)

    Article  MathSciNet  Google Scholar 

  76. D.W. Markiewicz: Survey on Symplectic Integrators (Univ. California, Berkeley 1999) preprint 

    Google Scholar 

  77. R. Mclachlan: Symplectic integration of hamiltonian wave equations, Numer. Math. 66, 465–492 (1994)

    Article  MathSciNet  Google Scholar 

  78. R. Courant, K. Friedrichs, H. Lewy: Über die partiellen Differenzengleichungen der mathematischen Physik, Math. Ann. 100(1), 32–74 (1928), https://doi.org/10.1007/BF01448839

    Article  MathSciNet  MATH  Google Scholar 

  79. L. Verlet: Computer ``experiments'' on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules, Phys. Rev. 159(1), 98–103 (1967)

    Article  Google Scholar 

  80. K.J. Bathe: Finite-Element Methoden (Springer, Berlin, Heidelberg 2002)

    Book  Google Scholar 

  81. M. Campbell, P. Campbell: The Science of String Instruments (Springer, New York 2010) pp. 301–315

    Book  Google Scholar 

  82. B. Geiser: Studien zur Frühgeschichte der Violine. In: Publikationen der Schweizerischen Musikforschenden Gesellschaft, Serie 2 (Gemeinsamer Bibliotheksverbund (GBV)/Verbundzentrale des GBV (VZG), Bern 1974)

    Google Scholar 

  83. D.D. Boyden: The History of Violin Playing from Its Origins to 1761, and Its Relationship to the Violin and Violin Music (Oxford Univ. Press, Oxford 1967)

    Google Scholar 

  84. K.C. Wali: Cremona Violins: A Physicist’s Quest for the Secrets of Stradivari (World Scientific, Hackensack 2010)

    Google Scholar 

  85. D. Ullmann: Chladni und die Entwicklung der Akustik von 1750–1860 (Birkhäuser, Basel 1996)

    Book  Google Scholar 

  86. H. von Helmholtz: Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik (Friedrich Vieweg und Sohn, Braunschweig 1896)

    MATH  Google Scholar 

  87. L. Cremer: Physik der Geige (Hirzel, Stuttgart 1981)

    Google Scholar 

  88. G. Bissinger, E.G. Williams, N. Valdivia: Violin f-hole contribution to far-field radiation via patch near-field acoustical holography, J. Acoust. Soc. Am. 121(6), 3899–3906 (2007)

    Article  Google Scholar 

  89. G. Bissinger: The Science of String Instruments (Springer, New York 2010) pp. 317–345

    Book  Google Scholar 

  90. H.N. Fletcher, T.D. Rossing: Physics of Musical Instruments, 2nd edn. (Springer, New York 2000)

    MATH  Google Scholar 

  91. C.M. Hutchins: Klang und Akustik der Geige, Spektrum Wiss. 2, 112–122 (1981)

    Google Scholar 

  92. J.-L. Florens: Expressive bowing on a virtual string instrument, Lect. Notes Comput. Sci. 2915, 487–496 (2004)

    Article  Google Scholar 

  93. M. Demoucron: On the Control of Virtual Violins – Physical Modelling and Control of Bowed String Instruments, PhD Thesis (Université Pierre et Marie Curie – Paris VI, Royal Institute of Technology, Stockholm 2008)

    Google Scholar 

  94. E. Maestre: Analysis/synthesis of bowing control applied to violin sound rendering via physical models, Proc. Meet. Acoust. 19(1), 3271 (2013)

    Google Scholar 

  95. J. Woodhouse, P.M. Galluzo: The bowed string as we know it today, Acta Acust. united Acust. 90, 579–589 (2004)

    Google Scholar 

  96. E. Bavu, J. Smith, J. Wolfe: Torsional waves in a bowed string, Acta Acust. united Acust. 91, 241–246 (2005)

    Google Scholar 

  97. A. Chaigne, A. Askenfelt: Numerical simulations of piano strings. I. A physical model for a struck string using finite difference methods, J. Acoust. Soc. Am. 95(2), 1112–1118 (1994)

    Article  Google Scholar 

  98. J. Bensa, S. Bilbao, R. Kronland-Martinet, J.O. Smith III: The simulation of piano string vibration: From physical models to finite difference schemes and digital waveguides, J. Acoust. Soc. Am. 114(2), 1095–1107 (2003)

    Article  Google Scholar 

  99. H.N. Fletcher, T.D. Rossing: The Physics of Musical Instruments (Springer, New York 1998)

    Book  Google Scholar 

  100. F. Pfeifle, R. Bader: Real-time finite-difference string-bow interaction field programmable gate array (fpga) model coupled to a violin body, J. Acoust. Soc. Am. 130(4), 2507–2507 (2011)

    Article  Google Scholar 

  101. J. Woodhouse: On the ‘‘bridge hill’’ of the violin, Acta Acust. united Acust. 91, 155–165 (2005)

    Google Scholar 

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Pfeifle, F. (2018). Real-Time Signal Processing on Field Programmable Gate Array Hardware. In: Bader, R. (eds) Springer Handbook of Systematic Musicology. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55004-5_20

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