Probabilities, Random Variables, and Random Processes: Digital and Analog |
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Page 80
... plotted in Figure 3.2c . The function i ( t ) may be written as x ( t + ) or ∞ Σ g ( t − 2n + p ) -∞ and this is the periodic function x ( t ) shifted units to the left , as shown plotted in Figure 3.2d . Using the definition i = iin ...
... plotted in Figure 3.2c . The function i ( t ) may be written as x ( t + ) or ∞ Σ g ( t − 2n + p ) -∞ and this is the periodic function x ( t ) shifted units to the left , as shown plotted in Figure 3.2d . Using the definition i = iin ...
Page 110
... plotted in Figure 4.5a . We notice the similarity of fx ( a ) to px ( a ) , the mass function . Instead of fx ( a ) containing discrete values , it has delta functions with the probabilities of the mass function as weighting factors ...
... plotted in Figure 4.5a . We notice the similarity of fx ( a ) to px ( a ) , the mass function . Instead of fx ( a ) containing discrete values , it has delta functions with the probabilities of the mass function as weighting factors ...
Page 168
... plotted in Figure 5.3b is fx ( a ) . Remembering Example 5.2 , X was the random variable describing choosing a ... Figure 5.3a ) 10 1 -da ( Notice Figure 5.3a ) fy ( B ) = [ * 0 da + [ ' 1o 40 = 3 20 For ẞ > 4 , fy ( B ) is obviously 0 ...
... plotted in Figure 5.3b is fx ( a ) . Remembering Example 5.2 , X was the random variable describing choosing a ... Figure 5.3a ) 10 1 -da ( Notice Figure 5.3a ) fy ( B ) = [ * 0 da + [ ' 1o 40 = 3 20 For ẞ > 4 , fy ( B ) is obviously 0 ...
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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