ECE 437 Digital Signal Processing I FALL 2005
Homework Assignment #5
Due: 4 October 2005
1. A continuous-time signal xa(t) has Fourier transform
-
6
¡¡¡@@@¡¡¡@@@¡¡¡@@@
−300 −250 −200 −150 −100 −50 50 100 150 200 250 300
1
2
0
Xa(F)
F(Hz)
Let x(n) = xa(nT ) (sampled version of xa(t) with sampling period T), and let X(ω)
be the DTFT of x(n). Sketch X(ω) for −π≤ω≤πwhen
(a) T= 1/300 sec.
(b) T= 1/400 sec.
(c) T= 1/500 sec.
2. If the discrete-time Fourier transform of x(n) is
-
6
−3π−
5π
2
−2π−
3π
2
−π−
π
2
π
2π3π
22π
5π
23π
100
200
X(ω)
ω
and T= 1/100 sec., sketch the Fourier transform Xa(Ω) of an analog signal xa(t) such
that x(n) = xa(nT ).
3. Problem 4.17(c)(d)(f) from the text.
4. Suppose that X(ω) is the DTFT of a real-valued signal x(n). Given Y(ω) = X(4ω),
express y(n) in terms of x(n).
5. Problem 4.19(a) from the text.
6. Problem 4.22(a)(b) from the text.