Answer Happy

1. Let a signal x[n] = {-1,0,3,1} be an input to an LTI system with the impulse response of h[n] = {1,0,1). (a) Find the output by using the convolution theorem (b) Find the output in Z-domain. To do that you need to find the X(z) and H(z) and then multiply them X(z)H(z), then take the inverse Z-transform. (C) What is the frequency response of this filter? Plot the magnitude and phase responses 2. Find the DTFT of x [n] = {1, 0, 2). 3. Find the DFT of x[n] = {1,0, 2). How is this related to the question 2? 4. Consider a cascaded system where two LTI filters are connected in series, i.e. the input x[n] goes through the first filter, with the impulse response of hi[n], and y1 (n) comes out, then y1 [n] is the input to the second filter, with the impulse response of h2[n], and produces y2[n]. If the impulse resonses are hin) (1, 0, 2) and h2[n] = (2, 1), then reduce these two filters into a single filter with the impulse response of hin. Compute h[n).