Probabilities, Random Variables, and Random Processes: Digital and Analog |
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Page 347
... zero - mean random process is a sta- tionary random process . ( b ) A weighted integral of a stationary zero - mean random process is a stationary random process . We say that the random process y ( t ) is the integral of x ( t ) if for ...
... zero - mean random process is a sta- tionary random process . ( b ) A weighted integral of a stationary zero - mean random process is a stationary random process . We say that the random process y ( t ) is the integral of x ( t ) if for ...
Page 352
... zero - mean random and uncorrelated Rxy ( T ) = Rƒƒ ( T ) * h ( T ) + Rnn ( T ) * h ( T ) or h ( T ) Rxx ( T ) + h ( T ) Rnn ( T ) Ryy ( T ) = Rƒƒ ( T ) * Cnn ( T ) + Rnn ( T ) * Cnn ( T ) CASE 2 A deterministic signal f ( t ) plus ...
... zero - mean random and uncorrelated Rxy ( T ) = Rƒƒ ( T ) * h ( T ) + Rnn ( T ) * h ( T ) or h ( T ) Rxx ( T ) + h ( T ) Rnn ( T ) Ryy ( T ) = Rƒƒ ( T ) * Cnn ( T ) + Rnn ( T ) * Cnn ( T ) CASE 2 A deterministic signal f ( t ) plus ...
Page 437
... zero - mean noise signal . DETERMINISTIC SIGNAL PLUS UNCORRELATED ZERO - MEAN NOISE ( CONTINUOUS CASE ) Table 8.7 shows a linear system with input x ( t ) = f ( t ) + n ( t ) . If the func- tion f ( t ) is deterministic and causal and ...
... zero - mean noise signal . DETERMINISTIC SIGNAL PLUS UNCORRELATED ZERO - MEAN NOISE ( CONTINUOUS CASE ) Table 8.7 shows a linear system with input x ( t ) = f ( t ) + n ( t ) . If the func- tion f ( t ) is deterministic and causal and ...
Contents
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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