Signal Processing and Linear Systems-B.P.Lathi copy

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Unformatted text preview: e delayed by t he s ame t ime i nterval t d. B ut if t he slope is n ot c onstant, t he t ime d elay t d varies with frequency. T his v ariation means t hat different frequency components u ndergo different a mounts o f t ime delay, a nd c onsequently t he o utput waveform will n ot b e a r eplica of t he i nput waveform. A good way t o j udge phase linearity is t o p lot t d as a function of frequency. For a distortionless system, t d s hould be c onstant over t he b and o f interest. I t is o ften t hought (erroneously) t hat flatness of a mplitude r esponse \H(w)\ a lone can g uarantee s ignal quality. However, a system m ay have a flat a mplitude r esponse a nd y et d istort a signal beyond recognition if t he p hase response is not linear ( td n ot c onstant). T he Nature o f Distortion in Audio and Video Signals G enerally s peaking, a h uman e ar c an r eadily perceive a mplitude d istortion, a lthough i t i s relatively insensitive t o p hase distortion. For t he p hase distortion t o b ecome noticeable, t he v ariation in delay [variation in t he s lope of LH(w)J s hould b e c omparable t o t he Signal d uration ( or t he physically perceptible d uration, in case t he s ignal i tself is long). I n t he case o f a udio signals, each spoken syllable can b e c onsidered as a n i ndividual signal. T he average d uration o f a spoken syllable is of a m agnitude o f t he o rder of 0.01 t o O.I.seconds. T he a udio systems m ay have nonlinear p hases, y et no noticeable signal distortion results because in practical audio s ystems, m aximum v ariation in t he slope of LH(w) is only a small fraction of a millisecond. T his is t he r eal t ruth u nderlying t he s tatement t hat " the h uman e ar is relatively insensitive t o p hase d istortion."3 As a result, t he m anufacturers o f audio e quipment m ake available only \H(w)\, t he a mplitude r esponse characteristic of t heir s ystems. F or v ideo signals, in c ontrast, t he s ituation is exactly t he o pposite. T he h uman eye is sensitive t o p hase distortion b ut is relatively insensitive t o a mplitude distortion. T he a mplitude d istortion in television signals manifests itself as a p artial d estruction o f t he r elative half-tone values of t he r esulting picture, which is n ot r eadily a pparent t o t he h uman eye. T he p hase distortion (nonlinear phase), on t he o ther h and, c auses different t ime delays in different picture elements. T he r esult is a smeared p icture, which is readily perceived by t he h uman eye. P hase d istortion is also very i mportant in digital communication systems because t he n onlinear phase c haracteristic o f a channel causes pulse dispersion (spreading o ut), which in t urn c auses pulses t o i nterfere w ith n eighboring pulses. This interference c an c ause a n e rror in t he p ulse a mplitude a t t he receiver: a b inary 1 m ay read as 0 , a nd vice versa. 4 .5 Ideal and practical filters I deal filters allow distortionless transmission of a certain b and o f frequencies a nd s uppress all t he r emaining fre...
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This note was uploaded on 04/14/2013 for the course ENG 350 taught by Professor Bayliss during the Spring '13 term at Northwestern.

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