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 B¡¦(»ý·«)
|