Suppose you get noisy measurements y[n] = ( 1) n x [n] + A[n] where x[n]
Question:
Suppose you get noisy measurements
y[n] = ( − 1)n x [n] + Aη[n]
where x[n] is the desired signal, and η[n] is a noise that varies from 0 to 1 at random.
(a) Let A = 0, and x[n] = sign[cos(0.7πn)]. Determine how to recover it from y[n]. Specify the type of filter you might need. Consider the first 100 samples of x[n] and use MATLAB to find the spectrum of x[n] and y[n] to show that the filter you recommend will do the job.
(b) Use MATLAB function fir 1 to generate the kind of filter you decided to use above (choose an order N > 40 to get good results) and show that when filtering y[n], for A = 0, you obtain the desired result.
(c) Consider the first 1000 samples of the MATLAB file handel a period of a signal that continuously replays these values over and over. Let x[n] be the desired signal that results from this. Now let A = 0.01, and use the function rand to generate the noise, and come up with suggestions as to how to get rid of the effects of the multiplication by (−1) n and of the noise η[n]. Recover the desired signal x[n].
Step by Step Answer:
ac To recover xn we need to demodulate yn by multiplying it by 1 n which gives a lowpass signal ...View the full answer
