Computer Engineering 4TL4: Digital Signal Processing (Fall 2003)
Solutions to Midterm Exam
1. Consider a discrete-time linear time-invariant system with impulse response h [ n ] . Show
that if the input x [ n ] is a periodic sequence with period N (i.e.,

COMP ENG 4TL4 Digital Signal Processing
Solutions to Homework Assignment #3
1. Consider an LTI system that is stable and for which H ( z ) , the z-transform of the impulse
response is given by:
H ( z) =
3
1 + 1 z 1
3
.
Suppose x [ n ] , the input to the s

COMP ENG 4TL4 Digital Signal Processing
Solutions to Homework Assignment #2
1. The impulse response of an LTI system is shown in Fig. 1 below. Determine and carefully
sketch the response of this system to the input x[n] = u[n 4].
(10 pts)
1
4 5
n
0 1 2 3

Computer Engineering 4TL4: Digital Signal Processing (Fall 2003)
Solutions to Final Exam
1. The step response y [ n ] of a causal, stable LTI system is:
y [n] = ( 1 ) u [n] ,
2
n
where u [ n ] is the unit step function.
a. Find the z-domain transfer funct

COMP ENG 4TL4 Digital Signal Processing
Solutions to Homework Assignment #1
1. Using the definition of linearity given in Lecture #5, show that the following two systems are
both linear.
a. The ideal-delay system, i.e., y[n] = Tacfw_x[n] = x[nnd], where n

COMP ENG 4TL4 Digital Signal Processing
Solutions to Homework Assignment #4
1. The figure below shows the pole-zero plot for a causal LTI system with a real-valued impulse
response. Indicate which of the following properties apply to this system, justifyi

COMP ENG 4TL4 Digital Signal Processing
Solutions to Homework Assignment #5
1. Four values of a stationary random process x[n] have been observed, giving the discrete-time
sequence v[n] = cfw_0.05, 0.3, 0.5, 1.
a. Use the autocorrelation-based method of s

Problem I
The system function of a stable discrete LSI system is
z+0.9
Hm : (z +1.1)(z 0.95)
a) Sketch the zplane diagram showing all pole and zero locations. What is
the ROC of
b) Determine the impulse response h(n) of the system.
0) Determine the