1.1.6 Make a sketch of each of the following signals
(a)
f ( n) =
1
X
( 0.9)
k
(n
3 k)
k=0
(b)
g ( n) =
1
X
( 0.9)
|k |
(n
3 k)
k= 1
(c)
x(n) = cos(0.25 n) u(n)
(d)
x(n) = cos(0.5 n) u(n)
1.1.6) Solution
11
1.2.1 A discrete-time system may be classied as
1.6.1 A causal discrete-time system is described by the dierence equation,
y ( n) = x ( n) + 3 x ( n
1) + 2 x(n
4)
(a) What is the transfer function of the system?
(b) Sketch the impulse response of the system.
1.6.1) Solution
H (z ) = 1 + 3 z
1
+ 2z
4
h(
1.3.7 Discrete-time signals f and g are dened as:
f ( n) = a n u ( n)
g ( n) = f ( n) = a
n
u ( n)
Find the convolution:
x(n) = (f g )(n)
Plot f , g , and x when a = 0.9. You may use a computer for plotting.
1.3.7) Solution
1
X
x ( n) =
=
f (k )g (n
k= 1
http:/www.youtube.com/watch?v=jGk3w1b7UXQ
http:/eeweb.poly.edu/iselesni/EL6113/misc/DataEOG.txt
http:/eeweb.poly.edu/iselesni/EL6113/
http:/www.youtube.com/watch?v=VLVjf9dUQjc (discrete time frequency response)
http:/www.youtube.com/watch?v=E3QfYXscsCc (d
EE 3054: Signals, Systems, and Transforms
Fall 2008
(b) Sketch the output signal, y (n), produced by the 4-point input signal,
x(n) illustrated below.
3
Test 1: Discrete-time Signals and Systems
2
x(n)
2
No notes, closed book
1
Show your work
Simplify
EE 3054: Signals, Systems, and Transforms
Fall 2007
3. Classify the system in Problem 2 as:
(a) causal/non-causal
Test 1
(b) linear/nonlinear
(c) time-invariant/time-varying
No notes, closed book
(d) stable/unstable
Show your work
Simplify your answers