Probabilities, Random Variables, and Random Processes: Digital and Analog |
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Page 129
... average value of each waveform , the mean square value of each waveform , and the rms value based on taking time averages . By definition , the time average of a waveform is 1 3 ( 1 ) = lim 27 Sy1 ( 1 ) dt y1 ( t ) where the symbol 22 T ...
... average value of each waveform , the mean square value of each waveform , and the rms value based on taking time averages . By definition , the time average of a waveform is 1 3 ( 1 ) = lim 27 Sy1 ( 1 ) dt y1 ( t ) where the symbol 22 T ...
Page 245
... averages or averages based on random variables sampling the process are equal to the corresponding time averages for ... average . x ( t ) or X is called the mean value of the random process . Another first - order equivalency is ∞ lime ...
... averages or averages based on random variables sampling the process are equal to the corresponding time averages for ... average . x ( t ) or X is called the mean value of the random process . Another first - order equivalency is ∞ lime ...
Page 313
... average basis as Rxx ( k ) = x ( n ) x ( n + k ) N 1 = lim 2 ∞ - N 2N + 1 Σ x , ( n ) x , ( n + k ) n = - N and ( 7.14 ) Lxx ( k ) = [ x ( n ) -x ] [ x ( n + k ) − x ] = lim b 。 N 2N + 1 -∞ - N 1 Σ [ x , ( n ) − x ] [ x , ( ...
... average basis as Rxx ( k ) = x ( n ) x ( n + k ) N 1 = lim 2 ∞ - N 2N + 1 Σ x , ( n ) x , ( n + k ) n = - N and ( 7.14 ) Lxx ( k ) = [ x ( n ) -x ] [ x ( n + k ) − x ] = lim b 。 N 2N + 1 -∞ - N 1 Σ [ x , ( n ) − x ] [ x , ( ...
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5 | 54 |
General Formulation and Solution of Problems | 69 |
Copyright | |
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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