DIGITAL SIGNAL PROCESSING: A Backward Glance and Emerging Paradigms

Kalasalingam University, Digital Signal Processing and Applications, Nondestructive Evaluation using Barkhausen NoiseV.K. Madan, PhDBTech (IITD), PhD (IITB), PDF (U. Sask., Canada)Fellow: IETE, IE (India); LM: INS, IPA, NTSI, ASI, ISTE

Senior ProfessorKalasalingam University Ex: Scientific Officer (H), Bhabha Atomic Research Centre, Mumbai Professor, Homi Bhabha National Institute , MumbaiProfessor, BITS, PilaniTeacher, PhD(Tech) Electronics Engrg, U of MumbaiResearch Board Member, Kalasalingam University

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KALASALINGAM UNIVERSITYKalasalingam Academy of Research and Education(under section 3 of UGC act 1956)Accredited by NAAC with B grade with CGPA of 2.81 on 4 point scaleTo Be a Centre of Excellence of International Repute in Education and ResearchTo Produce Technically Competent, Socially Committed Technocrats and Administrators Through Quality Education and ResearchMISSIONVISION3Global AssociationsCarnegie Mellon University, USAUniversity of Oklahoma, USABall State University, USAEast Tennessee State University, USA Georgetown University, USA University of Applied Sciences, Western SwitzerlandCentro De Investigacion Y De Estudios Avanzados Del IPN, Mexico INM Leibniz-Institute for New Materials gGmbH, H-66123 Saarbrucken, Germany Centre for Combinatorics, Nankai University, China Hannam University, South KoreaSoongsil University, South KoreaTechnical University of Kosice, The Slovak Republic

MoU with International Universities 4Science, Technology, Art, Religion, Music Earlier: One state scientist like Archimedes, Nobility, Professors, Common people Newton: Philosophy of Natural SciencePhilosophy: An obstinate attempt to think clearlyDisciplines, specializationMultidisciplinary, synthesis, fusion, merging of toolsHermann Hesse: The Glass Bead Game (Das Glasperlenspiel)Inspiration from Leonardo da Vinci: There is no man from whom I cant learn somethingMoral: Keep mind open to all disciplines and try to integrate them with your expertise. Respect the great people but question their work.

John Masefield(Poet Laureate)Adventure on, for, from the littlest clueHas come whatever worth man ever knew;The next to lighten all men may be youDigital Signal Processing (DSP) and Applications

What is DSP Used For?And much more!

What is DSP? Digital Signal Processing the processing or manipulation of signals using digital techniquesADCDACDigital Signal ProcessorAnalogue to Digital ConverterDigital to Analogue ConverterInput SignalOutput SignalTransformsTransforms -- a mathematical conversion from one way of thinking to another to make a problem easier to solve. Example: Logarithmic transformation transformsolutionin transformway of thinkinginversetransformsolution in original way of thinkingproblem in original way of thinkingDSP: Applied2012 IEEE Intl. Conf Emerging Signal Processing Applications (ESPA), Las Vegas (emerging applications)3D technology for gaming, telepresenceGesture recognition for games and natural user interfacesDigital photography4G wirelessRoboticsMultimedia tabletsSP in automobiles: speech interfaces, camerasVoice searchSP with multicore processorsIPTV

Dogma of Circle DSPThe Greek Philosopher PlatoClaudius Ptolemy (all the phenomena in the sky are produced by uniform and circular motion)Eudoxus: superposition of rotating spheres. Aristotle used upto 54 spheresClaudius Ptolemy replaced spheres by circlesVasco da Gamma IndiaColumbus AmericaMagellan worldNicholas CopernicusLuther: fool Johannes Kepler

Propagation of the Dogma of CircleAstronomy (disappeared) reappeared in Physics (eit) Electrical Engineering (ejt)Phasor: first used by Lord Raleigh in soundPhasor: introduced in EE by Oliver HeavisidePopularized by Kennelly and Steinmetz in USA in early 1900s. Still very important.Sinusoids are bread and butter of EEECircle: Astronomy to Power System,DSP, Communication EngineeringPower System: Phasor AnalysisDSP: unit circle in the complex planeCommunication Engineering: modulator

Modulatoror mixerFaith vs Reason in ScienceLast 100 years Fourier transforms are being used. Only uses for which the transforms are good are developed. Selective development. However it generated lot of knowledge base.Arthur Koestler: The sleepwalkers (challenges the habitual idea of a progressive science)Fourier transforms:Dont converge at discontinuity (Gibbs). Information intensive points: discontinuities.requires infinite sinusoidal waves.Noncausal: O/p before I/pNegative frequency

Faith vs Reason in Science (contd.)Fermat conjectured in 1640 that all the Fermat numbers (22m + 1 ) are prime. In 1732 Euler pointed out that the Fermat number 4294967297 was not prime. (90 years) (Fermat numbers are useful in DSP)Minsky and Papert published from MIT in 1969 a book Perceptron and wrote "...our intuitive judgment that the extension (to multilayer systems) is sterile. In simple language it means that multilayer perceptron cannot realize Exclusive-OR gate. The research in neural networks was halted for 10 years until it was proved that their judgement was wrong. (10 years).

FactsJ. Finlaisons report to House of Commons, London 1829 (used digital filter)Many digital filters with excellent properties were existing in 19th century.FFT algorithm existed (1805) before Fourier transform (1822). Rediscovered in 1965.Fourier transform remained questionable till a paper by Norbert Wiener from MIT in 1930.Spread spectrum communication invented by by Hollywood actress Lamarr and composer Antheil. Used by US Navy during Cuba blocade by President Kennedy

Fourier TheoryFourier introduced the idea of representing an arbitrary periodic function as a trigonometric series, eminent mathematicians such as Lagrange resisted it.Till 1930 : Fourier theory was useful for analyzing periodic and aperiodic functions, but not for random functions. Norbert Wiener from MIT in 1930 applied Fourier theory for analyzing random functions. Presently it is known as Wiener-Khinchin theorem'' stating that the power spectrum is the Fourier transform of signals autocorrelation function.

Fast FourierTransform (FFT)C.F. Gauss had written in 1805, 'Experience will teach the user that this method will greatly lessen the tedium of mechanical calculation.' this method is FFT. It was rediscovered by Cooley and Tukey in 1965."The FFT rediscovery has been called the most important numerical algorithm of our lifetime (Strang, 1994)." (Kent & Read 2002, 61)

A Peep Beyond Fourier TransformNumerous orthogonal transforms exist other than Fourier transform. Fourier transform is, however, most popular and most widely used compared to any other transform.Walsh-Hadamard transformNumber theoretic transformHartley transformHouseholder transformand many more . . . Third Century Chinese Verseby Sun Tzu(useful in Computers)We have things of which we do not know the number,If we count them by three, the remainder is 2,If we count them by five, the remainder is 3,If we count them by seven, the remainder is 2,How many things are there?..

Moduli: 3, 5, 7Remainders: 2, 3, 2Answer: 23

Sanskrit, Vedic Arithematic(useful in computer Science)Multiply: 1 1 1 by 1 1 1Answer: 1 2 3 2 1 Trick: ascending, descending, symmetry

Square: (52) x (52)Answer: 2704 (mental time 5 seconds)

Trick: any number 30 to 7050/2 = 25+2 = 27 and 2x2 = 4

Evariste Galoiss work is useful in DSP

Cochlea: A bank of filtersHuman ears do not hear wave-like oscillations, but constant tone

Often it is easier to work in the frequency domain(for cochlear animation: http://www.rockefeller.edu/labheads/hudspeth/movie06_popup.html )

Analog, Discrete-time, and Digital Signal y(t) = A sin (2ft + )Analog signal?Discrete time signal?

Digital signal: t and y(t) are quantized

Signal ClassificationPeriodic and aperiodicDeterminstic and randomEnergy and powerAnalog and digitalType I and Type II (new classification)New Classification of Digital Signals:Type I and Type II (Madan et al) Type I and Type II; based on fundamental problems of aliasing and quantization noise (q.n.). The classification has enhanced the scope of DSP in many disciplines:

Type I: aliasing and q.n. are addressed along the abscissa and ordinate respectively Type II: aliasing and q.n. are addressed along the abscissaType I and Type II SignalsType II: Nuclear spectra like gamma, x-ray spectra, population sciences etc.DSP methods widely used for Type I signals, are generally not used for Type II signals. DSP methods have demonstrated numerous advantages for processing Type II signals, . Presently not many Type II signals are processed employing DSP.DSP Applications DevelopedNuclear Spectral ProcessingPower Transformers (Maximum Entropy Spectral Analysis)Population SciencesElectric ArcsSpeech ProcessingMagnetic Barkhausen Noise

Speech ProcessingBill Gates and Speech Technology Bill Gates : Microsoft is pushing touchscreen and speech technology to replace keyboards

Speech signal Hood and TF Analysis

Speech Coding PredictionA(z)s(n)+d(n)se(n)d(n)A(z)++se(n)sr(n)

Transmit errorGamma Radiation and its UsesMedical UsesAcademic and Scientific ApplicationsIndustrial UsesNuclear Power PlantA Gamma Ray Spectrum

Fourier Transforms of the Spectra

SAMPO has 25,000 lines of FORTRAN, 10,000 lines of C, and 12,000 lines of assembler(DSP based: