Homework 4 (ECE220  Fall 2007)
•
Due:
Thursday, October 4 at the beginning of lecture.
•
Reasoning and work must be shown to gain full/partial credit.
•
WRITE YOUR NAME AND NET ID ON ALL PAGES HANDED IN!
1.
(25 points) Convolution and power
Suppose you have a linear time invariant system with
impulse response
h
[
n
] and you feed it with an input signal that has a certain energy
E
x
<
∞
. A
reasonable question to ask is what is the energy
E
y
of the signal that comes out of the system,
say
y
[
n
].
The same question applies for analog LTI systems with impulse response
h
(
t
), with input
x
(
t
) and output
y
(
t
). Since analog systems usually model physical systems, the ability of the
system to transfer energy at its output must be important. Obviously the same question can
be asked for the power of a signal, if the signal is a signal with bounded power but not bounded
energy (a so called
signal of power
, as deﬁned in class).
First think about this intuitively: do you think an LTI system should treat all signals with
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '05
 JOHNSON
 Digital Signal Processing, Signal Processing, LTI system theory, Impulse response, analog signal Rx, analog LTI systems

Click to edit the document details