ECE 310 Digital Signal Processing
Homework 9
1. A 3.0 sec. segment of {xa(t)}3.0
t=0 = cos(0.2πt) is sampled at a rate of 1/T = 30 Hz. The resulting
90 samples are zero padded to 128 and the DFT {X[k]}127
k=0 is computed. Determine k0 such that
X[k0]≥X[k] for k = 0, 1, ··· , 63.
2. Assume that xa(t) = L
=1 A cos(Ωt), where the A have positive values. We further assume
that xa(t) is measured at t = nT for T = 1/8 second and n = 0, 1,…, 63 to obtain {xn}63
n=0 =
{xa(nT)}63
n=0. The 64point DFT of {xn}63
n=0 is represented by {Xk}63
k=0, whose magnitude is shown
in the figure below.
0 8 16 24 32 40 48 56 63 0
16
32
48
64
80
96 Xk

DFT frequencies
Determine L, and A and Ω for = 1, 2,…,L.
3. Complete the following signal flow diagram (butterfly structure) of a 4pt, radix2, decimationintime FFT algorithm. Specify all the connection weights and determine the indexes (a, b, c, and d)
of the input signal sequence.
X
xa
xb
c
3
X0
X1
x X2
xd