Communication Systems and Techniques by Mischa Schwartz

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By Mischa Schwartz

An introductory, graduate-level examine glossy communications commonly and radio communications particularly. This seminal presentation of the purposes of conversation thought to sign and receiver layout brings you invaluable insights into the basic techniques underlying contemporary communications platforms, specially instant communications.Coverage contains: AM, FM part Modulation, PCM, fading, and variety receivers.This is a vintage reissue of a booklet released through McGraw Hill in 1966.

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It is useful to demonstrate this property at this point, since it will be appropriate in dealing with multiple signal samples in the next section, in which case we shall find ourselves considering sums of logarithms of likelihood ratios. Consider, then, two extreme cases: 1. 'Y« 1: then r is likely to be small also, and 10 (r;) == 1 + (;~y == er'~/2N rA« 1 N (2-1-14) Taking the natural log, as in Eq. (2-1-13), r2'Y > 'Y > 2N 2N r2 or Thus, for small 'Y the (2-1-15) likelihood test reduces to that of using a quadratic STATISTICAL COMMUNICATION THEORY 53 envelope detector, and the output must exceed twice the mean-squared noise at the input.

C. r) Gx( f ) G~(f) : = Rx(r) s, (f ) Rx~(O):O The random variable x(t) and its Hilbert transform are thus uncorrelated at a given instant of FIG. 1-6-4. Hilbert-transform relatime. This is apparent from the fact that tions for a random process. since Rz('1') is even in '1', "R:t('1') must be odd, or "R:t(O) = o. This fact will be particularly useful in rederiving the envelope statistics of noise, using the Hilbert-transform formulation. d. (1-6-26) (1-6-27) Here Rt('1') represents the autocorrelation function of the analytic signal or preenvelope z(t) = x(t) + j£(t) (1-6-28) The proof of Eq.

The Fourier transform of z(t) is, from Eq. 5) (This represents the action of the phase shifter. ) 31 GENERAL TUTORIAL MATERIAL Introducing Eq. (1-6-5) into (1-6-4) we get, Z(w) = { ~X(w) w~O w

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