Question -

1- Derive the decimation-in-frequency radix-2, N-point FFT. You only need to show a couple of stages to demonstrate the idea. Provide a schematic diagram for N=8. Please answer with clarity and be concise (stay within 2 pages)

2- A causal filter H(z) is excited by x(n) which is a white noise signal of zero mean and unit variance. Its Output is y(n).

H(z) = z/z + 0.9

Give the autocorrelation of y(n) in closed form; show all your work. Give numerical values for r_yy(0), r_yy(1) r_yy(2) (Do not exceed one page).

This is the textbook we use - "Required Text: Digital Signal Processing - An Interactive Approach, A. Spanias 2nd Edition "