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a power * A random process X(t) has Spectral density given by Sxx (w) = Su-we...
2. (30 points) Let X(t) be a wide-sense stationary (WSS) random signal with power spectral density S(f) = 1011(f/200), and let y(t) be a random process defined by Y(t) = 10 cos(2000nt + 1) where is a uniformly distributed random variable in the interval [ 027]. Assume that X(t) and Y(t) are independent. (a) Derive the mean and autocorrelation function of Y(t). Is Y(t) a WSS process? Why? (b) Define a random signal Z(t) = X(t)Y(t). Determine and sketch the...
Q.6 Determine the autocorrelation function and power spectral density of the random process olt)= m(t) cos(21f t+), where m(t) is wide sense stationary random process, and is uniformly distributed over (0,2%) and independent of m(t).
Problem 4 Let X(t), a continuous-time white noise process with zero mean and power spectral density equal to 2, be the input to an LTI system with impulse response h(t)- 0 otherwise of Y (t). Sketch the autocorrelation function of Y(t) Problem 4 Let X(t), a continuous-time white noise process with zero mean and power spectral density equal to 2, be the input to an LTI system with impulse response h(t)- 0 otherwise of Y (t). Sketch the autocorrelation function...
process x(t) Question4 (15 points): A random telegraph signal is a taking the values +1 and -1 as f+1 1-1 wheret,is a set of Poisson points with average density a) Determine the mean and autocorrelation of x(t). b) Judge whether x(t) is Wide Sense Stationary, why? c) Determine the Power Spectral Density S(w) of x(t)
11.8 A linear system has a transfer function given by H(W) + 15w+50 Determine the power spectral density of the output when the input function is a. a stationary random process X(t) with an autocorrelation function, Rxx(t)=10e ! b. white noise that has a mean-square value of 1.2 V/Hz
Assume we have a constant spectral power density of S W/m2-nm. Using this and the equation for Spectral Responsivity derive an equation that yields the short circuit current density as a function of band gap.
1. Show that if X(t) is a real random process with finite mean power and a mean power spectral density function Sx(S), then for all f. (a) Sx(f) > 0: (b) Sx(-f)=Sx(f). Hint: Recall that if x(t) is a real signal with spectrum X(f), then X (f) = X(-).
Problem 5 A Wide-sense stationary random process X(t), with mean value 10 and power spectrum Sxx = 15078(0) +3/[1 + (0/2)?] is applied to a network with impulse response h(t) = 10exp(-4/11) Find (a) H(o) for the network (b) the mean value of the response (C) Syy(Q), the power spectrum of the response
Power Spectral Density of Signal A signal s(t) can be expressed as the following equation: L-1 where L is a positive integer. {An}n=0 are independent and identically distributed (i.i.d.) discrete random variables. The probability mass function (PMF) of An is An() 0 otherwise, where A is a positive constant in volt. To is a uniformly distributed random variable with probability density function (PDF) defined by 0. otherwise. L-1 To and {An}n=d are independent. The signal p(t) is a pulse and...
Q1. A DSB-SC signal is transmitted over a noisy channel with power spectral density of noise given as, 0, otherwise with B-200 kHz and N 10W Hz. The message bandwidth is 10 kHz and its average power is 10 W. Assume A,-1, 100kHz, and the channel attenuates signal power by a factor of 1000 (-30 dB). Assume that a suitable band-pass filter is used at the receiver to limit out-of-band noise. (a) Determine the average signal power at the receiver...