Massachusetts Institute of Technology
Department of Electrical Engineering and Computer Science
6.111 – Introductory Digital Systems Laboratory
Problem Set 3
Problem Set Issued:
March 3, 2004
Problem Set Due:
March 19, 2004
Comments:
This problem set is intended to prepare you for Laboratory 3 which is a Finite
Impulse Response (FIR) filter. Problem 1 is intended to familiarize you with the concepts of
convolution and filtering. While we do not expect you to have a background in signals (6.003 is
not a prerequisite) we would like for you to have an appreciation for how digital filtering works.
Problem 1: Convolution
An FIR filter uses convolution to generate the data points for the filtered output. Convolutions are
a weighted accumulation of sampled points from a signal. Given that h[n] is the Finite Impulse
response for a specific filter and x[nk] is the k
th
recent sample, the equation that best describes
the convolution we are going to implement is
N
−
1
y n
[
]
[
−
[ ]
=
h
k
x
n
k
]
∑
k
=
0
where
N
is the number of points in the convolution. Given the filter shown below compute the
convolution with the following inputs
h[n]
5
0 1 2 3 4
1
1
2
2
n
Part (a)
x1[n]
0 1 2
1
1
n
1
Part (b)
x2[n]
0
2
1
1
n
3
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Part (c)
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '04
 Prof.AnanthaChandrakasan
 Computer Science, Electrical Engineering, QU, Finite impulse response, Twos Complement Multiplier

Click to edit the document details