Probabilities, Random Variables, and Random Processes: Digital and Analog |
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Page 341
... impulse response h ( t ) the output y ( t ) is y ( t ) = h ( t ) * x ( t ) or x ( t ) * h ( t ) Figure 7.19 The output of a continuous linear system with impulse response h ( t ) . SOLUTION ( a ) For this circuit , H ( s ) = 1 / s 1+ ...
... impulse response h ( t ) the output y ( t ) is y ( t ) = h ( t ) * x ( t ) or x ( t ) * h ( t ) Figure 7.19 The output of a continuous linear system with impulse response h ( t ) . SOLUTION ( a ) For this circuit , H ( s ) = 1 / s 1+ ...
Page 342
... impulse response h ( n ) the output y ( n ) is y ( n ) = h ( n ) * x ( n ) = Σ h ( k ) x ( n − k ) all k = Σh ( n - k ) x ( k ) all k ( 7.48 ) This output may be realized by delay elements , amplifiers , and summing devices . An analog ...
... impulse response h ( n ) the output y ( n ) is y ( n ) = h ( n ) * x ( n ) = Σ h ( k ) x ( n − k ) all k = Σh ( n - k ) x ( k ) all k ( 7.48 ) This output may be realized by delay elements , amplifiers , and summing devices . An analog ...
Page 433
... impulse response and the discrete pulse response , respectively . When dealing with two real functions f ( t ) and g ( t ) , one of which is even - say , f ( t ) = f ( t ) -then the following relations hold for the Fourier transforms F ...
... impulse response and the discrete pulse response , respectively . When dealing with two real functions f ( t ) and g ( t ) , one of which is even - say , f ( t ) = f ( t ) -then the following relations hold for the Fourier transforms F ...
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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