Determine the variance, autocorrelation, and PSD
h(n) 0.2(0.8)n
H(z) =
Determine the variance, autocorrelation, and PSD h(n) 0.2(0.8)n H(z) = 0.2 10.82 1 0.2 10.82 1
Determine the variance, autocorrelation, and PSD h(n) 0.2(0.8)n H(z) = 0.2 10.82 1
The following causal system is excited by white noise (x(n)=w(n)) of zero mean and unit variance. The output is y(n). q(n)=x(n) - 0.8 q(n-1) y(n)=0.2 q(n) a) Determine the autocorrelation of the output y(n) in closed form for all m. Give numerical values for ryy(0), ryy(1), ryy(2). b) Find the variance of y(n). Give a numerical value and show all your work. c) Find the poles and zeros of the power spectral density (PSD) of y(n) and sketch them carefully...
A causal filter H(z) is excited by x(n) which is a white noise signal of zero mean 2 and unit variance. Its output is y(n). (28 points) H(2)05 Z-0.9 Give the autocorrelation of y(n) in closed form. Show all your work Give numerical values for ryy(0).1(1).1(2) a. b. Give the variance of y(n). c. Give the power spectral density (PSD) of y(n). d. A causal filter H(z) is excited by x(n) which is a white noise signal of zero mean...
2. The following causal system is excited by white noise (x[n)=w(n)) of zero mean and unit variance. The output is y(n). q(n)-x(n) 0.8 q(n-1) y(n) 0.2 q(n) a) Determine the autocorrelation of the output y(n) in closed form for all m. Give numerical values for ry(0), ryy(1), ryy(2) b) Find the variance of y(n). Give a numerical value and show all your work. c) Find the poles and zeros of the power spectral density (PSD) of y(n) and sketch them...
e.) Find and sketch the PSD of V(t). What does the system in Fig. 1 do? Problem 4 (10 points, Graduate Students Only). Suppose X is a binary random variable, with PIX = ol = 0.8 and PIX = 1] = 0.2. Suppose Y is a Gaussian random variable conditioned on X. Specifically, when X 0, py)x (ulz) is a Gaussian distribution with 0 mean and variance σ2. Similarly, when X-1, prix(ylz) Is a Gaussian distribution with mean A (A...
2. For two systems with impulse responses hi[n] (0.2) u[n] h2[n] - (0.8) ul-n - 1] and Write down the transfer functions Hi(z) and H2(z). Include their ROCs as well and plot the pole-zero diagram for each.
Determine and plot the autocorrelation function rxx[l] of the signal 1, 0≤n≤N−1 x[n] = 0, otherwise . Determine and plot the autocorrelation function r] of the signal x[n] = 0, otherwise
(42)1+ (z-0.5)z-0.9)(z-0.8) 3. The transfer function of a system is H(z) = a) Compute an analytical expression for the response y[n] if x[n] = u[n]. . Use Matlab to calculate the coefficients b) Simulate the response using Matlab (stem plot). Generate 50 points. (enter transfer function into Matlab and apply step input) (42)1+ (z-0.5)z-0.9)(z-0.8) 3. The transfer function of a system is H(z) = a) Compute an analytical expression for the response y[n] if x[n] = u[n]. . Use Matlab...
Problem 1: What is the variance of a portfolio with: w1 =0.2, w2 =0.8, σ12 =10, σ22 =20, and σ12 =5. Problem 2: a) If the stocks 1 and 2 have negative correlation 12 then their covariance σ12 is also negative. Yes, no, uncertain. Explain. b) If stocks 1 and 2 are uncorrelated, i.e. 12=0 then their covariance is zero, Yes, no, uncertain. Explain c) If stocks 1 and 2 have variance σ2=16 each, could their covariance be equal to...
Xew) 0.8 F 0.6 Consider -0.2 -1 -0.8 -0.6 -0.4 -0. 2 0 0.2 0.4 0.6 0.8 w (x21) the following plot of X(ew. Calibrate the frequency axis to the true (analog) frequency N = Fow if the sampling rate used was F, = 500Hz.