consider the following input signals:
1.) x1[n]=u[n], x2[n]=(cosn)u[n], x3[n]=(1+r[n])u[n]
where r[n] is random sequence with zero mean and unit variance. Compute the response y[n], with each of the three signals, for each the two systems, for n=0....50, using two methods, CONV and FILTER. Plot the results(12 plots) and show that the results obtained with CONVolution and FILTER are identical. Determine the transient and the steady-state parts of the responses wherever possible.
consider the
Note: CONV will give you 100 samples of the output. The second 50 samples are irrevant, just ignore them, WHY?
2) consider the discrete linear time invariant system
y[n]+a1y[n-1]+a2y[n-2]=b1x[n-1]+b2x[n-2],
where b1=1, b2= -0.7, S1:a1= -1.4, a2=0.48 S2: a1=1.4, a2=0.48
write a program that implement the system difference equation recursively, in "real-time" fashion, including the recursive update of variable samples(shift register). Compute and plot the response to x2[n] and x3[n], for one of the two systems, for n =0...50(use zero initial conditions and make sure you are using the exact same random sequence as in Problem 1(They should be the same). What is the difference between the two approaches("real-time" vs. FILTER) ?