Introduction (Vaseghi - Advanced Digital Signal Processing and Noise Reduction)

Advanced Digital Signal Processing and Noise Reduction, Second Edition.Saeed V. VaseghiCopyright © 2000 John Wiley & Sons LtdISBNs: 0-471-62692-9 (Hardback): 0-470-84162-1 (Electronic)1HELLOINTRODUCTION1.1 Signals and Information1.2 Signal Processing Methods1.3 Applications of Digital Signal Processing1.4 Sampling and Analog−to−Digital ConversionSignal processing is concerned with the modelling, detection,identification and utilisation of patterns and structures in a signalprocess. Applications of signal processing methods include audio hifi, digital TV and radio, cellular mobile phones, voice recognition, vision,radar, sonar, geophysical exploration, medical electronics, and in generalany system that is concerned with the communication or processing ofinformation. Signal processing theory plays a central role in thedevelopment of digital telecommunication and automation systems, and inefficient and optimal transmission, reception and decoding of information.Statistical signal processing theory provides the foundations for modellingthe distribution of random signals and the environments in which the signalspropagate.

Statistical models are applied in signal processing, and indecision-making systems, for extracting information from a signal that maybe noisy, distorted or incomplete. This chapter begins with a definition ofsignals, and a brief introduction to various signal processing methodologies.We consider several key applications of digital signal processing in adaptivenoise reduction, channel equalisation, pattern classification/recognition,audio signal coding, signal detection, spatial processing for directionalreception of signals, Dolby noise reduction and radar.

The chapter concludeswith an introduction to sampling and conversion of continuous-time signalsto digital signals.2Introduction1.1 Signals and InformationA signal can be defined as the variation of a quantity by which informationis conveyed regarding the state, the characteristics, the composition, thetrajectory, the course of action or the intention of the signal source.

A signalis a means to convey information. The information conveyed in a signal maybe used by humans or machines for communication, forecasting, decisionmaking, control, exploration etc. Figure 1.1 illustrates an information sourcefollowed by a system for signalling the information, a communicationchannel for propagation of the signal from the transmitter to the receiver,and a signal processing unit at the receiver for extraction of the informationfrom the signal.

In general, there is a mapping operation that maps theinformation I (t ) to the signal x (t ) that carries the information, this mappingfunction may be denoted as T[·] and expressed asx(t )=T [ I (t )](1.1)For example, in human speech communication, the voice-generatingmechanism provides a means for the talker to map each word into a distinctacoustic speech signal that can propagate to the listener. To communicate aword w, the talker generates an acoustic signal realisation of the word; thisacoustic signal x(t) may be contaminated by ambient noise and/or distortedby a communication channel, or impaired by the speaking abnormalities ofthe talker, and received as the noisy and distorted signal y(t).

In addition toconveying the spoken word, the acoustic speech signal has the capacity toconvey information on the speaking characteristic, accent and the emotionalstate of the talker. The listener extracts these information by processing thesignal y(t).In the past few decades, the theory and applications of digital signalprocessing have evolved to play a central role in the development of moderntelecommunication and information technology systems.Signal processing methods are central to efficient communication, and tothe development of intelligent man/machine interfaces in such areas asNoiseInformationsourceInformation tosignal mappingSignalNoisysignalChannelSignal &Digital Signal InformationProcessorFigure 1.1 Illustration of a communication and signal processing system.Signal Processing Methods3speech and visual pattern recognition for multimedia systems.

In general,digital signal processing is concerned with two broad areas of informationtheory:(a) efficient and reliable coding, transmission, reception, storage andrepresentation of signals in communication systems, and(b) the extraction of information from noisy signals for patternrecognition, detection, forecasting, decision-making, signalenhancement, control, automation etc.In the next section we consider four broad approaches to signal processingproblems.1.2 Signal Processing MethodsSignal processing methods have evolved in algorithmic complexity aimingfor optimal utilisation of the information in order to achieve the bestperformance.

In general the computational requirement of signal processingmethods increases, often exponentially, with the algorithmic complexity.However, the implementation cost of advanced signal processing methodshas been offset and made affordable by the consistent trend in recent yearsof a continuing increase in the performance, coupled with a simultaneousdecrease in the cost, of signal processing hardware.Depending on the method used, digital signal processing algorithms canbe categorised into one or a combination of four broad categories.

These arenon−parametric signal processing, model-based signal processing, Bayesianstatistical signal processing and neural networks. These methods are brieflydescribed in the following.1.2.1 Non−parametric Signal ProcessingNon−parametric methods, as the name implies, do not utilise a parametricmodel of the signal generation or a model of the statistical distribution of thesignal. The signal is processed as a waveform or a sequence of digits.Non−parametric methods are not specialised to any particular class ofsignals, they are broadly applicable methods that can be applied to anysignal regardless of the characteristics or the source of the signal.

Thedrawback of these methods is that they do not utilise the distinctcharacteristics of the signal process that may lead to substantial4Introductionimprovement in performance. Some examples of non−parametric methodsinclude digital filtering and transform-based signal processing methods suchas the Fourier analysis/synthesis relations and the discrete cosine transform.Some non−parametric methods of power spectrum estimation, interpolationand signal restoration are described in Chapters 9, 10 and 11.1.2.2 Model-Based Signal ProcessingModel-based signal processing methods utilise a parametric model of thesignal generation process.

The parametric model normally describes thepredictable structures and the expected patterns in the signal process, andcan be used to forecast the future values of a signal from its past trajectory.Model-based methods normally outperform non−parametric methods, sincethey utilise more information in the form of a model of the signal process.However, they can be sensitive to the deviations of a signal from the class ofsignals characterised by the model.

The most widely used parametric modelis the linear prediction model, described in Chapter 8. Linear predictionmodels have facilitated the development of advanced signal processingmethods for a wide range of applications such as low−bit−rate speech codingin cellular mobile telephony, digital video coding, high−resolution spectralanalysis, radar signal processing and speech recognition.1.2.3 Bayesian Statistical Signal ProcessingThe fluctuations of a purely random signal, or the distribution of a class ofrandom signals in the signal space, cannot be modelled by a predictiveequation, but can be described in terms of the statistical average values, andmodelled by a probability distribution function in a multidimensional signalspace. For example, as described in Chapter 8, a linear prediction modeldriven by a random signal can model the acoustic realisation of a spokenword.

However, the random input signal of the linear prediction model, orthe variations in the characteristics of different acoustic realisations of thesame word across the speaking population, can only be described instatistical terms and in terms of probability functions. Bayesian inferencetheory provides a generalised framework for statistical processing of randomsignals, and for formulating and solving estimation and decision-makingproblems. Chapter 4 describes the Bayesian inference methodology and theestimation of random processes observed in noise.Applications of Digital Signal Processing51.2.4 Neural NetworksNeural networks are combinations of relatively simple non-linear adaptiveprocessing units, arranged to have a structural resemblance to thetransmission and processing of signals in biological neurons.

In a neuralnetwork several layers of parallel processing elements are interconnectedwith a hierarchically structured connection network. The connection weightsare trained to perform a signal processing function such as prediction orclassification. Neural networks are particularly useful in non-linearpartitioning of a signal space, in feature extraction and pattern recognition,and in decision-making systems. In some hybrid pattern recognition systemsneural networks are used to complement Bayesian inference methods. Sincethe main objective of this book is to provide a coherent presentation of thetheory and applications of statistical signal processing, neural networks arenot discussed in this book.1.3 Applications of Digital Signal ProcessingIn recent years, the development and commercial availability of increasinglypowerful and affordable digital computers has been accompanied by thedevelopment of advanced digital signal processing algorithms for a widevariety of applications such as noise reduction, telecommunication, radar,sonar, video and audio signal processing, pattern recognition, geophysicsexplorations, data forecasting, and the processing of large databases for theidentification extraction and organisation of unknown underlying structuresand patterns.