Probabilities, Random Variables, and Random Processes: Digital and Analog |
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Page 150
Digital and Analog Michael O'Flynn. PROBLEMS 1. Consider the random phenomenon of rolling a tetrahedral die and if ... Consider the random phenomenon of tossing a coin three times . Define the random variable X such that X takes on a ...
Digital and Analog Michael O'Flynn. PROBLEMS 1. Consider the random phenomenon of rolling a tetrahedral die and if ... Consider the random phenomenon of tossing a coin three times . Define the random variable X such that X takes on a ...
Page 227
... Consider the periodic waveform ∞ x ( t ) = Σ g ( t − 3n ) n an integer where g ( t ) = 1 -∞ 0 < t < l Consider the random phenomenon of sampling this waveform at t = t and t = 1 + , where t is uniformly chosen , 0 < t < 3 . Define the ...
... Consider the periodic waveform ∞ x ( t ) = Σ g ( t − 3n ) n an integer where g ( t ) = 1 -∞ 0 < t < l Consider the random phenomenon of sampling this waveform at t = t and t = 1 + , where t is uniformly chosen , 0 < t < 3 . Define the ...
Page 362
... Consider the random process with memory where every b s a pulse is generated with value + 1 or - 1. If the value of a pulse is + 1 , then the probability of the next pulse being +1 is ; whereas if the value of a pulse is -1 , then the ...
... Consider the random process with memory where every b s a pulse is generated with value + 1 or - 1. If the value of a pulse is + 1 , then the probability of the next pulse being +1 is ; whereas if the value of a pulse is -1 , then the ...
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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