Project Part | for ECE-4850 & BME7026-Signals Winter 2022 Consider a WSS process that consists of a signal s(n) plus additive white noise: x(n) = s(n) + (2), where w(n) is the white noise with variance of o7

Project Part | for ECE-4850 & BME7026-Signals
Winter 2022

Consider a WSS process that consists of a signal s(n) plus additive white noise:
x(n) = s(n) + (2), where w(n) is the white noise with variance of o7 . Consider the case when

s(n) = cos 2nf,n + acos 2nf,n + 0.2 cos 2nf3n
Derive the formula for signal to noise ratio (SNR) of x/n). Hint: You can use autocorrelation
function evaluate it at time zero; autocorrelation of a sinusoid was derived in class in Sept.
The goal is to investigate estimates of f; and /2 using power spectral density (PSD) for a finite
data record of N points. As a benchmark compare the spectral estimates obtained by Welch
and Periodogram methods.
Part LA
Select a=2. f1=0.25627, {?=0.26877, and /3=0.3. sampling rate of | and a o7=2.5. Use N =
256 points. Then, estimate the PSD of the signal with Weltch (using three windows:
rectangular, Hamming and Hanning) and Peridogram; then, change the noise records to have
the same signal but with a different 0; = 5 and compare the results. In each case, calculate the
SNR.
Part I.B
Second, create another signal with a@=2, f=0.15627, /2=0.16877 and f:=0.3, and same SNRs
as before. Repeat Part A.
Write Up
Your report should include a brief but concise introduction followed by results and discussion.
Label each graph clearly with a complete caption.