Probabilities, Random Variables, and Random Processes: Digital and Analog |
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Page 361
... otherwise and fo ( a ) = 1⁄2 0 < a < 2 = 0 otherwise 3. Is m , ( t ) , the mean function of a random process , an even function ? If your answer is no , give a specific counterexample . 4. Consider the random process x ( t ) = A sin ...
... otherwise and fo ( a ) = 1⁄2 0 < a < 2 = 0 otherwise 3. Is m , ( t ) , the mean function of a random process , an even function ? If your answer is no , give a specific counterexample . 4. Consider the random process x ( t ) = A sin ...
Page 364
... otherwise and q ( t ) = e t t > 0 = 0 otherwise Make sketches to find the ranges of t for which r ( t ) , Cpp ( t ) , and Cpq ( t ) exist and sketch the final results . 17. If a function p ( t ) of width W1 ( that is , p ( t ) is ...
... otherwise and q ( t ) = e t t > 0 = 0 otherwise Make sketches to find the ranges of t for which r ( t ) , Cpp ( t ) , and Cpq ( t ) exist and sketch the final results . 17. If a function p ( t ) of width W1 ( that is , p ( t ) is ...
Page 509
... otherwise For t = 1 x ( p −t ) = p - 2 ; 1 < p < 2 = 0 otherwise For t = 4 x ( p - 1 ) = p - 5,4 < p < 5 = 0 ( b ) In general otherwise - x ( t − p ) = −p + t − 1 ; t − 1 < p < t = 0 otherwise ( Plot it ) For t = 3 x ( t − p ) ...
... otherwise For t = 1 x ( p −t ) = p - 2 ; 1 < p < 2 = 0 otherwise For t = 4 x ( p - 1 ) = p - 5,4 < p < 5 = 0 ( b ) In general otherwise - x ( t − p ) = −p + t − 1 ; t − 1 < p < t = 0 otherwise ( Plot it ) For t = 3 x ( t − p ) ...
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5 | 54 |
General Formulation and Solution of Problems | 69 |
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A₁ autocorrelation function average axiom B₁ balls Chapter convolution correlation integrals cross-correlation cross-correlation function cumulative distribution function dadß defined definition delta function denoted derivation deterministic discrete Fourier transform discrete probability theory discrete random process DRILL SET ensemble ergodic evaluate event space Example finite first-order stationary formula fundamental theorem fxy(a fy(B fz(y given impulse response joint density function joint mass function Laplace transform linear system M₁ member waveform notation obtained otherwise output periodic function periodic waveform permutations plotted in Figure points power spectral density probability measure probability theory problem properties pulse px(a random input random phenomenon range Rxx(T sample description space sampled values second-order stationary set theory shown in Figure shown plotted signal sketch SOLUTION solved statistics Sxx(w Ticket Pays two-sided Laplace transform two-sided z transform typical member X₁ z transform zero-mean