ECE130B
February 8, 2010
Home work 6
Cheat sheet
. You probably want to assemble most of the formulae in this home work into your cheat
sheet for the midterms and the ±nals. Your cheat sheet can only contain formulae and properties; no
proofs, or procedures, or example problems, are allowed.
Convolution
. The convolution of two discrete signals
x
[
n
]
and
h
[
n
]
is given by the formula
x
[
n
]
*
h
[
n
] =
s
k
=
∞
∞
x
[
k
]
h
[
n

k
]
.
Standard functions
.
•
Discrete delta function:
δ
[
n
] =
b
1
, n
= 0
,
0
, n
0
.
•
Discrete unit step function:
u
[
n
] =
b
1
, n
g
0
,
0
, n <
0
.
Reading
. Read chapter 2 of the text book, especially the parts on discrete signals and systems.
Exercise 1.
Show the following properties:
•
x
[
n
]
*
h
[
n
] =
h
[
n
]
*
x
[
n
]
(commutative).
•
(
αx
[
n
])
*
h
[
n
] =
α
(
x
[
n
]
*
h
[
n
])
(scaling).
•
(
x
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 Winter '08
 Staff
 Digital Signal Processing, NZ, Heaviside step function

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