ECEN 644 ADVANCED DIGITAL SIGNAL
http:/www.comm.utoronto.ca/~dkundur/course/discrete-time-systems/
PROCESSING
HOMEWORK #1 - SOLUTIONS
1.2
For a sinusoid of the form x(n ) = A cos( n + ) , the frequency can be expressed as
f =
.
2
Definition B1 from the te
http:/www.comm.utoronto.ca/~dkundur/course/discrete-time-systems/
ECEN 644 HOMEWORK #5
SOLUTION SET
7.1
x n is a real valued sequence. The first five points of its 8-point DFT are:
cfw_0.25, 0.125 - j0.3018, 0, 0.125 - j0.0518, 0
To compute the 3 remainin
ECEN 644 ADVANCED DIGITAL
SIGNAL PROCESSING
http:/www.comm.utoronto.ca/~dkundur/course/discrete-time-systems/
HOMEWORK #2 - SOLUTIONS
2.13
The input-output equation of a relaxed LTI system is known to be
y (m ) =
x(n ) h(m n ) =
n =
x(m n ) h(n )
n =
To
ECEN 644 ADVANCED DIGITAL
SIGNAL PROCESSING
http:/www.comm.utoronto.ca/~dkundur/course/discrete-time-systems/
HOMEWORK #4 - SOLUTIONS
6.1
We are given x a (t ) X a (F ) = 0 for F > B . Lets use as an example the following
function X a (F ) :
We know that
http:/www.comm.utoronto.ca/~dkundur/course/discrete-time-systems/
ECEN 644 ADVANCED DIGITAL SIGNAL
PROCESSING
HOMEWORK #3 - SOLUTIONS
4.13
Recall that the Fourier transform X ( ) of a signal x(n ) is given by:
X ( ) = F [x(n )] =
x(n ) exp( jn )
n =
Ther
http:/www.comm.utoronto.ca/~dkundur/course/discrete-time-systems/
ECEN644 - Homework 7
Solutions
11.9
x(k)
v1(n)
I
D
y1(m)
System A
x(k)
v2(n)
D
I
y2(m)
System B
System A:
v1 [n] =
y1 [m] =
=
x[ n ] n = 0, I, 2I,
I
0 otherwise
(1)
x[ mD ] mD = 0, I, 2I,
http:/www.comm.utoronto.ca/~dkundur/course/discrete-time-systems/
ECEN644 - Homework 8
Solutions
13.1
If plant output d(n) is corrupted by white noise w(n), let y(n) = d(n) + w(n).
Let output of the system model be
M 1
h(k)x(n k)
y (n) =
k=0
N
2
n=0 e (n)
ECEN 644 HOMEWORK #6
SOLUTION SET
http:/www.comm.utoronto.ca/~dkundur/course/discrete-time-systems/
11.1
(a)
Lets assume that the original spectrum X a F has a triangular shape with amplitude L (see figure).
X F , being a sampled version of X a F for FS 2