Probabilities, Random Variables, and Random Processes: Digital and Analog |
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Page 388
... Laplace transforms . Chn ( T ) , the correlation time transfer func- tion , will always possess a two - sided Laplace transform if the impulse response approaches zero for infinite positive time . ( Does this always happen ? ) In ...
... Laplace transforms . Chn ( T ) , the correlation time transfer func- tion , will always possess a two - sided Laplace transform if the impulse response approaches zero for infinite positive time . ( Does this always happen ? ) In ...
Page 389
... transform is box ( t ) + · + bm dm x input x ( t ) drm Y ( s ) = H ( s ) X ( s ) or the output or system function is ... Laplace transform in continuous system analysis . and for t < 0 , y ( t ) = 0 The one - sided Laplace transform is ...
... transform is box ( t ) + · + bm dm x input x ( t ) drm Y ( s ) = H ( s ) X ( s ) or the output or system function is ... Laplace transform in continuous system analysis . and for t < 0 , y ( t ) = 0 The one - sided Laplace transform is ...
Page 402
... Laplace transforms are almost identical , why bother with both ? " The answer is that Laplace and Fourier transforms are like two different languages . The Laplace transform deals with a pole - zero interpretation of signals , whereas ...
... Laplace transforms are almost identical , why bother with both ? " The answer is that Laplace and Fourier transforms are like two different languages . The Laplace transform deals with a pole - zero interpretation of signals , whereas ...
Contents
1 | 3 |
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