Question

Consider a linear time-invariant system with impulse response hin (-1, n o 2, n 1 h[n]--1, n=2 0, otherwise (a) Determine the system frequency response H(e"). Then compute the magnitude and (b) Does the system have a linear phase? Briefly explain your answer. (2 marks) (c) Compute the system output yin] for all values of n if the input r[n] has the form of: phase of H(e (6 marks) 1,n=1 2, n 2 n3, n 3 4, n-4 0, otherwise (6 marks) (d) Compute yinl for all values of n if rnl ufnl. Is y/n] an infinite-duration sequence? (6 marks

Answer 1

a. Find the solution in the image below:

The phase and magnitude plot can be obtained using the comman ezplot in MATLAB:

Magnitude plot:

Phase plot:

b. This can be observed from the phase plot obtained above, that the phase of the given system is linear.

c.

d.