신호처리기말.pdf

Question 1 [20%]:
Determine all possible signals x[n] associated with the z-transform X(z) = (1 5z 1 2z 1)(3 z 1) .

Question 2 [25%]:
Determine the coe cients {h[n]} of a high-pass linear-phase FIR lter of length L = M + 1 = 4 which has an antisymmetric impulse response, i.e. h[n] = h[M n], and a frequency response H(e|!) that satises the condition |H(ej/4)| = 0.5 and |H(ej3/4)| = 1.

Question 3 [35%]:
Consider the two systems shown in the gure below.

xc (t)
Ideal A/D

x[n]
Squaring

x2 [n]
Ideal D/A

y1 (t)

Fs

Fs

xc (t)
Squaring

x2 (t) c
Ideal A/D

v[n]
Ideal D/A

y2 (t)

Fs

Fs

a) Find analytic relations between the signals y1 (t) and xc (t), as well as between y2 (t) and xc (t) for the case of Fs = 2B Hz (with B ` 0) and (1, |F | B Xc (|F) = 0, otherwise. b) Determine y1 (t) and y2 (t) if xc (t) = cos(2F0 t) with F0 = 20 Hz and Fs = 50 Hz. c) Repeat part (b) for Fs = 30 Hz.

2

Question 4 [20%]:
Dene the N -point DFT of the Blackma…