Noise and Distortion (779814), страница 3
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The spectrum of the drilling noise shownin Figure 2.8(a) reveals that most of the noise energy is concentrated in thelower-frequency part of the spectrum. In fact, it is true of most audio signalsand noise that they have a predominantly low-frequency spectrum.However, it must be noted that the relatively lower-energy high-frequencypart of audio signals plays an important part in conveying sensation andquality. Figures 2.9(a) and (b) show examples of the spectra of car noiserecorded from a BMW and a Volvo respectively.
The noise in a car isnonstationary, and varied, and may include the following sources:(a) quasi-periodic noise from the car engine and the revolving mechanicalparts of the car;(b)noise from the surface contact of wheels and the road surface;(c) noise from the air flow into the car through the air ducts, windows,sunroof, etc;(d) noise from passing/overtaking vehicles.The characteristic of car noise varies with the speed, the road surfaceconditions, the weather, and the environment within the car.The simplest method for noise modelling, often used in current practice,is to estimate the noise statistics from the signal-inactive periods. In optimalBayesian signal processing methods, a set of probability models are trainedfor the signal and the noise processes. The models are then used for thedecoding of the underlying states of the signal and noise, and for noisysignal recognition and enhancement.Noise and Distortion422.10.1 Additive White Gaussian Noise Model (AWGN)In communication theory, it is often assumed that the noise is a stationaryadditive white Gaussian (AWGN) process.
Although for some problems thisis a valid assumption and leads to mathematically convenient and usefulsolutions, in practice the noise is often time-varying, correlated and nonGaussian. This is particularly true for impulsive-type noise and for acousticnoise, which are non-stationary and non-Gaussian and hence cannot bemodelled using the AWGN assumption.
Non-stationary and non-Gaussiannoise processes can be modelled by a Markovian chain of stationary subprocesses as described briefly in the next section and in detail in Chapter 5.2.10.2 Hidden Markov Model for NoiseMost noise processes are non-stationary; that is the statistical parameters ofthe noise, such as its mean, variance and power spectrum, vary with time.Nonstationary processes may be modelled using the hidden Markov models(HMMs) described in detail in Chapter 5.
An HMM is essentially a finitestate Markov chain of stationary subprocesses. The implicit assumption inusing HMMs for noise is that the noise statistics can be modelled by aMarkovian chain of stationary subprocesses. Note that a stationary noiseprocess can be modelled by a single-state HMM. For a non-stationary noise,a multistate HMM can model the time variations of the noise process with afinite number of stationary states. For non-Gaussian noise, a mixtureGaussian density model can be used to model the space of the noise withineach state. In general, the number of states per model and number ofmixtures per state required to accurately model a noise process depends ona = α01a = α11S0ka =1 - α00S1a =1 - α10(a)(b)Figure 2.10 (a) An impulsive noise sequence.
(b) A binary-state model of impulsivenoise.Bibliography43the non-stationary character of the noise.An example of a non-stationary noise is the impulsive noise of Figure2.10(a). Figure 2.10(b) shows a two-state HMM of the impulsive noisesequence: the state S0 models the “impulse-off” periods between theimpulses, and state S1 models an impulse. In those cases where each impulsehas a well-defined temporal structure, it may be beneficial to use a multistate HMM to model the pulse itself.
HMMs are used in Chapter 11 formodelling impulsive noise, and in Chapter 14 for channel equalisation.BibliographyBELL D.A. (1960) Electrical Noise and Physical Mechanism. Van Nostrand,London.BENNETT W.R. (1960) Electrical Noise. McGraw-Hill. NewYork.DAVENPORT W.B. and ROOT W.L. (1958) An Introduction to the Theory ofRandom Signals and Noise. McGraw-Hill, New York.GODSILL S.J. (1993) The Restoration of Degraded Audio Signals.
Ph.D.Thesis, Cambridge University.SCHWARTZ M. (1990) Information Transmission, Modulation and Noise. 4thEd., McGraw-Hill, New York.EPHRAIM Y. (1992) Statistical Model Based Speech Enhancement Systems.Proc. IEEE 80, 10, pp. 1526–1555.VAN-TREES H.L. (1971) Detection, Estimation and Modulation Theory.Parts I, II and III. Wiley, New York..
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