(c) Find the pdf of X(0). (d) The process X(t) is passed through an ideal bandpass filter with transfer function given by otherwise. Let Y(t) denote the output process. Find the power of Y(t), i.e., find E(Y(t)2.
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3.34. Let (X.(t) and (x.(e)) denote two statistically independent zero mean stationary Gaussian r...
3.34. Let fXc(t)) and (X,(t)J denote two statistically independent zero n stationary Gaussian random processes with...
3.34. Let fXc(t)) and (X,(t)J denote two statistically independent zero n stationary Gaussian random processes with common power spec- tral density given by SX (f) = SX (f) = 112B(f) watt/Hz. Define x(t) = Xe(t) cos(2tht)--Xs(t) sin(2tht) where fo 》 (a) Is X(t) a Gaussian process? (b) Find the mean E(X (t), autocorrelation function Rx (t,t + T), and power spectral density Sx(f) of the process X(t) (c) Find the pdf of X(O) (d) The process X(t) is passed through...
5.57 Let np(t) be a zero-mean white Gaussian noise with the power spectral density 20 let this noise be passed through an ideal bandpass filter with the bandwidth 2W centered at the frequency fe...
5.57 Let np(t) be a zero-mean white Gaussian noise with the power spectral density 20 let this noise be passed through an ideal bandpass filter with the bandwidth 2W centered at the frequency fe. Denote the output process by nt). 1. Assuming fo fe, find the power content of the in-phase and quadrature components of n(t). We were unable to transcribe this image
5.57 Let np(t) be a zero-mean white Gaussian noise with the power spectral density 20 let this...
Problem 20 Let X(t) be a white Gaussian noise with Sx(f)= No. Assume that X(t) is...
Problem 20 Let X(t) be a white Gaussian noise with Sx(f)= No. Assume that X(t) is input to a bandpass filter with frequency response 1<|f] < 3 2 H(f) = < otherwise Let Y(t) be the output. a. Find Sy(f). b. Find Ry(7). c. Find E[Y(t)²].
1) Random Processes: Suppose that a wide-sense stationary Gaussian random process X (t) is input to the filter shown below. The autocorrelation function of X(t) is 2xx (r) = exp(-ary Y(t) X(t) Delay...
1) Random Processes: Suppose that a wide-sense stationary Gaussian random process X (t) is input to the filter shown below. The autocorrelation function of X(t) is 2xx (r) = exp(-ary Y(t) X(t) Delay a) (4 points) Find the power spectral density of the output random process y(t), ΦΥΥ(f) b) (1 points) What frequency components are not present in ΦYYU)? c) (4 points) Find the output autocorrelation function Фуу(r) d) (1 points) What is the total power in the output process...
1) Random Processes: Suppose that a wide-sense stationary Gaussian random process X (t) is input to...
1) Random Processes: Suppose that a wide-sense stationary Gaussian random process X (t) is input to the filter shown below. The autocorrelation function of X(t) is 2xx (r) = exp(-ary Y(t) X(t) Delay a) (4 points) Find the power spectral density of the output random process y(t), ΦΥΥ(f) b) (1 points) What frequency components are not present in ΦYYU)? c) (4 points) Find the output autocorrelation function Фуу(r) d) (1 points) What is the total power in the output process...
Q1) Let X(t) be a zero-mean WSS process with X(t) is input to an LTI system with Let Y(t) be the output. a) Find the mean of Y(t) b) Find the PSD of the output SY(f) c) Find RY(0) -----------------...
Q1) Let X(t) be a zero-mean WSS process with X(t) is input to an LTI system with Let Y(t) be the output. a) Find the mean of Y(t) b) Find the PSD of the output SY(f) c) Find RY(0) ------------------------------------------------------------------------------------------------------------------------- Q2) The random process X(t) is called a white Gaussian noise process if X(t) is a stationary Gaussian random process with zero mean, and flat power spectral density, Let X(t) be a white Gaussian noise process that is input to...
The random process X(t) is defined by X(t) = X cos 27 fot + Y sin...
The random process X(t) is defined by X(t) = X cos 27 fot + Y sin 2 fot, where X and Y are two zero-mean Gaussian random variables, each with the variance 02. (a) Find ux(t) (b) Find RX(T). Is X(t) stationary? (c) Repeat (a) and (b) for 0 + 0
Problem 1 (10 Marks) The noise X(t) applied to the filter shown in Figure I is...
Problem 1 (10 Marks) The noise X(t) applied to the filter shown in Figure I is modeled as a WSS random process with PSD S,(f). Let Y(t) denote the random noise process at the output of the filter. A linea filsee Figure 1: The Filter. (T) Je Sinc 1. Find the frequency response, H(f), of the filter. 2. If X(t) is a white noise process with PSD No/2, find the PSD of the noise precess Y(t). 2- f 3. Is...
Let X(t) and Y(t) be independent, wide-sense stationary random process with zero means and the same covariance function...
Let X(t) and Y(t) be independent, wide-sense stationary random process with zero means and the same covariance function Cx(t) Let Z(t) be defined by Z(t) = X(t)coswt + Y(t)sinwt Find the joint pdf of X(t1) and X(t2) in part b
Let x(t) = Acos(27/0t + ?) where fo is a given constant, A is a Rayleigh...
Let x(t) = Acos(27/0t + ?) where fo is a given constant, A is a Rayleigh random variable with ? is a uniformly distributed random variable on [0, 2n, and A and ? are statistically independent. a) Find the mean E[X (t)h b) Find the autocorrelation function E(X(t)X(t+)). c) Is (X(t)) wide-sense stationary? d) Find the power spectral density Sx(f)
3.34. Let fXc(t)) and (X,(t)J denote two statistically independent zero n stationary Gaussian random processes with common power spec- tral density given by SX (f) = SX (f) = 112B(f) watt/Hz. Define x(t) = Xe(t) cos(2tht)--Xs(t) sin(2tht) where fo 》 (a) Is X(t) a Gaussian process? (b) Find the mean E(X (t), autocorrelation function Rx (t,t + T), and power spectral density Sx(f) of the process X(t) (c) Find the pdf of X(O) (d) The process X(t) is passed through...
5.57 Let np(t) be a zero-mean white Gaussian noise with the power spectral density 20 let this noise be passed through an ideal bandpass filter with the bandwidth 2W centered at the frequency fe. Denote the output process by nt). 1. Assuming fo fe, find the power content of the in-phase and quadrature components of n(t). We were unable to transcribe this image
5.57 Let np(t) be a zero-mean white Gaussian noise with the power spectral density 20 let this...
Problem 20 Let X(t) be a white Gaussian noise with Sx(f)= No. Assume that X(t) is input to a bandpass filter with frequency response 1<|f] < 3 2 H(f) = < otherwise Let Y(t) be the output. a. Find Sy(f). b. Find Ry(7). c. Find E[Y(t)²].
1) Random Processes: Suppose that a wide-sense stationary Gaussian random process X (t) is input to the filter shown below. The autocorrelation function of X(t) is 2xx (r) = exp(-ary Y(t) X(t) Delay a) (4 points) Find the power spectral density of the output random process y(t), ΦΥΥ(f) b) (1 points) What frequency components are not present in ΦYYU)? c) (4 points) Find the output autocorrelation function Фуу(r) d) (1 points) What is the total power in the output process...
1) Random Processes: Suppose that a wide-sense stationary Gaussian random process X (t) is input to the filter shown below. The autocorrelation function of X(t) is 2xx (r) = exp(-ary Y(t) X(t) Delay a) (4 points) Find the power spectral density of the output random process y(t), ΦΥΥ(f) b) (1 points) What frequency components are not present in ΦYYU)? c) (4 points) Find the output autocorrelation function Фуу(r) d) (1 points) What is the total power in the output process...
The random process X(t) is defined by X(t) = X cos 27 fot + Y sin 2 fot, where X and Y are two zero-mean Gaussian random variables, each with the variance 02. (a) Find ux(t) (b) Find RX(T). Is X(t) stationary? (c) Repeat (a) and (b) for 0 + 0
Problem 1 (10 Marks) The noise X(t) applied to the filter shown in Figure I is modeled as a WSS random process with PSD S,(f). Let Y(t) denote the random noise process at the output of the filter. A linea filsee Figure 1: The Filter. (T) Je Sinc 1. Find the frequency response, H(f), of the filter. 2. If X(t) is a white noise process with PSD No/2, find the PSD of the noise precess Y(t). 2- f 3. Is...
Let x(t) = Acos(27/0t + ?) where fo is a given constant, A is a Rayleigh random variable with ? is a uniformly distributed random variable on [0, 2n, and A and ? are statistically independent. a) Find the mean E[X (t)h b) Find the autocorrelation function E(X(t)X(t+)). c) Is (X(t)) wide-sense stationary? d) Find the power spectral density Sx(f)
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