A narrow-band Gaussian noise process is sampled at the Nyquist rate. The samples

Question

A narrow-band Gaussian noise process is sampled at the Nyquist rate. The samples of the complex envelope of this process are given by n^-k = u_1^k + jn_Q^k where {n_l^k} and {n_Q^k} are independent, white Gaussian random variables with variance sigma^2 = 1. These samples are processes by the discrete-time filter y^-k + 1 = ay^-k + n^-k using the following Matlab script clear a = 0.8; sigma = 1; K = 1000; n = sigma + randn(K, 1) + J middot sigma middot randn (K, 1); y = filter (1, (1 - a], n); (a) What is mean and variance of output? (b) Is the output Gaussian? Justify your answer from simulation results and theoretically. (c) What is the discrete-time autocorrelation function of the filter output?

Explanation / Answer

clc;
clear all;
close all;

a = 0.8;
sigma = 1;

K = 1000;
n = sigma*randn(K,1) + j*sigma*randn(K,1);
y = filter(1, [1-a],n);

mean_y = mean(y)
abs_mean = abs(mean_y)
var_y = var(y)
%MEAN AND VARIANCE

hist(abs(y))
%HISTOGRAM FOLLOWS BELL CURVE

figure
y_corr = autocorr(y);
stem(y_corr);
%AUTOCORRELATION OUTPUT

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.