Noise and Distortion (779814), страница 2
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These variations may be attributed to the non-linear characteristics ofthe playback mechanism.2.5 Transient Noise PulsesTransient noise pulses often consist of a relatively short sharp initial pulsefollowed by decaying low-frequency oscillations as shown in Figure 2.6.The initial pulse is usually due to some external or internal impulsiveinterference, whereas the oscillations are often due to the resonance of then(m)m(a)(b)Figure 2.6 (a) A scratch pulse and music from a gramophone record. (b) Theaveraged profile of a gramophone record scratch pulse.36Noise and Distortioncommunication channel excited by the initial pulse, and may be consideredas the response of the channel to the initial pulse.
In a telecommunicationsystem, a noise pulse originates at some point in time and space, and thenpropagates through the channel to the receiver. The noise pulse is shapedby the channel characteristics, and may be considered as the channel pulseresponse. Thus we should be able to characterize the transient noise pulseswith a similar degree of consistency as in characterizing the channelsthrough which the pulses propagate.As an illustration of the shape of a transient noise pulse, consider thescratch pulses from a damaged gramophone record shown in Figures 2.6(a)and (b). Scratch noise pulses are acoustic manifestations of the response ofthe stylus and the associated electro-mechanical playback system to a sharpphysical discontinuity on the recording medium. Since scratches areessentially the impulse response of the playback mechanism, it is expectedthat for a given system, various scratch pulses exhibit a similarcharacteristics.
As shown in Figure 2.6(b), a typical scratch pulse waveformoften exhibits two distinct regions:(a) the initial high-amplitude pulse response of the playback system tothe physical discontinuity on the record medium, followed by;(b) decaying oscillations that cause additive distortion. The initial pulseis relatively short and has a duration on the order of 1–5 ms, whereasthe oscillatory tail has a longer duration and may last up to 50 ms ormore.Note in Figure 2.6(b) that the frequency of the decaying oscillationsdecreases with time. This behaviour may be attributed to the non-linearmodes of response of the electro-mechanical playback system excited by thephysical scratch discontinuity.
Observations of many scratch waveformsfrom damaged gramophone records reveals that they have a well-definedprofile, and can be characterised by a relatively small number of typicaltemplates. Scratch pulse modelling and removal is considered in detain inChapter 13.2.6 Thermal NoiseThermal noise, also referred to as Johnson noise (after its discoverer J.
B.Johnson), is generated by the random movements of thermally energisedparticles. The concept of thermal noise has its roots in thermodynamics andis associated with the temperature-dependent random movements of freeThermal Noise37particles such as gas molecules in a container or electrons in a conductor.Although these random particle movements average to zero, the fluctuationsabout the average constitute the thermal noise. For example, the randommovements and collisions of gas molecules in a confined space producerandom fluctuations about the average pressure. As the temperatureincreases, the kinetic energy of the molecules and the thermal noiseincrease.Similarly, an electrical conductor contains a very large number of freeelectrons, together with ions that vibrate randomly about their equilibriumpositions and resist the movement of the electrons.
The free movement ofelectrons constitutes random spontaneous currents, or thermal noise, thataverage to zero since in the absent of a voltage electrons move in alldifferent directions. As the temperature of a conductor, provided by itssurroundings, increases, the electrons move to higher-energy states and therandom current flow increases.
For a metallic resistor, the mean squarevalue of the instantaneous voltage due to the thermal noise is given byv 2 = 4kTRB(2.6)where k=1.38×10–23 joules per degree Kelvin is the Boltzmann constant, T isthe absolute temperature in degrees Kelvin, R is the resistance in ohms andB is the bandwidth. From Equation (2.6) and the preceding argument, ametallic resistor sitting on a table can be considered as a generator ofthermal noise power, with a mean square voltage v 2 and an internalresistance R. From circuit theory, the maximum available power deliveredby a “thermal noise generator”, dissipated in a matched load of resistance R,is given by2v2v PN = i 2 R = rms R == kTB4R 2R ( W)(2.7)where v rms is the root mean square voltage.
The spectral density of thermalnoise is given bykT(W/Hz)(2.8)PN ( f ) =2From Equation (2.8), the thermal noise spectral density has a flat shape, i.e.thermal noise is a white noise. Equation (2.8) holds well up to very high13radio frequencies of 10 Hz.Noise and Distortion382.7 Shot NoiseThe term shot noise arose from the analysis of random variations in theemission of electrons from the cathode of a vacuum tube. Discrete electronparticles in a current flow arrive at random times, and therefore there will befluctuations about the average particle flow.
The fluctuations in the rate ofparticle flow constitutes the shot noise. Other instances of shot noise are theflow of photons in a laser beam, the flow and recombination of electrons andholes in semiconductors, and the flow of photoelectrons emitted inphotodiodes. The concept of randomness of the rate of emission or arrival ofparticles implies that shot noise can be modelled by a Poisson distribution.When the average number of arrivals during the observing time is large, thefluctuations will approach a Gaussian distribution.
Note that whereasthermal noise is due to “unforced” random movement of particles, shot noisehappens in a forced directional flow of particles.Now consider an electric current as the flow of discrete electric charges.If the charges act independently of each other the fluctuating current is givenbyINoise(rms) = ( 2eIdcB )1/2(2.9)where e = 1.6 × 10 −19 coulomb is the electron charge, and B is themeasurement bandwidth. For example, a “steady” current Idc of 1 amp in abandwidth 1 MHz has an rms fluctuation of 0.57 microamps.
Equation (2.9)assumes that the charge carriers making up the current act independently.That is the case for charges crossing a barrier, as for example the current in ajunction diode, where the charges move by diffusion; but it is not true formetallic conductors, where there are long-range correlations between chargecarriers.2.8 Electromagnetic NoiseVirtually every electrical device that generates, consumes or transmitspower is a potential source of electromagnetic noise and interference forother systems.
In general, the higher the voltage or the current level, and thecloser the proximity of electrical circuits/devices, the greater will be theinduced noise. The common sources of electromagnetic noise aretransformers, radio and television transmitters, mobile phones, microwavetransmitters, ac power lines, motors and motor starters, generators, relays,oscillators, fluorescent lamps, and electrical storms.Channel Distortions39Electrical noise from these sources can be categorized into two basictypes: electrostatic and magnetic. These two types of noise arefundamentally different, and thus require different noise-shielding measures.Unfortunately, most of the common noise sources listed above producecombinations of the two noise types, which can complicate the noisereduction problem.Electrostatic fields are generated by the presence of voltage, with orwithout current flow.
Fluorescent lighting is one of the more commonsources of electrostatic noise. Magnetic fields are created either by the flowof electric current or by the presence of permanent magnetism. Motors andtransformers are examples of the former, and the Earth's magnetic field is aninstance of the latter. In order for noise voltage to be developed in aconductor, magnetic lines of flux must be cut by the conductor.
Electricgenerators function on this basic principle. In the presence of an alternatingfield, such as that surrounding a 50/60 Hz power line, voltage will beinduced into any stationary conductor as the magnetic field expands andcollapses. Similarly, a conductor moving through the Earth's magnetic fieldhas a noise voltage generated in it as it cuts the lines of flux.2.9 Channel DistortionsOn propagating through a channel, signals are shaped and distorted by thefrequency response and the attenuating characteristics of the channel. Thereare two main manifestations of channel distortions: magnitude distortionand phase distortion.
In addition, in radio communication, we have theInputOutputChannel distortionX(f)H(f)Y(f)=X(f)H(f)Noninvertible InvertibleNoninvertibleChannelnoisef(a)f(b)f(c)Figure 2.7 Illustration of channel distortion: (a) the input signal spectrum, (b) thechannel frequency response, (c) the channel output.Noise and Distortion40multi-path effect, in which the transmitted signal may take several differentroutes to the receiver, with the effect that multiple versions of the signalwith different delay and attenuation arrive at the receiver. Channeldistortions can degrade or even severely disrupt a communication process,and hence channel modelling and equalization are essential components ofmodern digital communication systems. Channel equalization is particularlyimportant in modern cellular communication systems, since the variations ofchannel characteristics and propagation attenuation in cellular radio systemsare far greater than those of the landline systems.
Figure 2.7 illustrates thefrequency response of a channel with one invertible and two non-invertibleregions. In the non-invertible regions, the signal frequencies are heavilyattenuated and lost to the channel noise. In the invertible region, the signal isdistorted but recoverable. This example illustrates that the channel inversefilter must be implemented with care in order to avoid undesirable resultssuch as noise amplification at frequencies with a low SNR. Channelequalization is covered in detail in Chapter 15.2.10 Modelling NoiseX(f) Magnitude (dB)The objective of modelling is to characterise the structures and the patternsin a signal or a noise process. To model a noise accurately, we need astructure for modelling both the temporal and the spectral characteristics ofthe noise.
Accurate modelling of noise statistics is the key to high-qualitynoisy signal classification and enhancement. Even the seemingly simple taskof signal/noise classification is crucially dependent on the availability ofgood signal and noise models, and on the use of these models within aBayesian framework. Hidden Markov models described in Chapter 5 aregood structure for modelling signals or noise.One of the most useful and indispensable tools for gaining insight intothe structure of a noise process is the use of Fourier transform for frequency0-802000(a)Frequency (Hz)4000(b)Figure 2.8 Illustration of: (a) the time-waveform of a drill noise, and (b) the frequencyspectrum of the drill noise.Modelling Noise4100-5-5-10-15dB-20N(f)N(f)dB-10-15-25-30-35-20-25-30-35-40-45-40-50-450125037502500Frequency (Hz)(a)400001250250037504000Frequency (Hz)(b)Figure 2.9 Power spectra of car noise in (a) a BMW at 70 mph, and(b) a Volvo at 70 mph.analysis. Figure 2.8 illustrates the noise from an electric drill, which, asexpected, has a periodic structure.
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