辅导 ELEC 224、讲解 Matlab编程语言
Matlab Laboratory (ELEC 224)
Session II: Convolution
1. Overview
The objective of this assignment is to gain some experience in writing Matlab code by
creating a Matlab function that performs a convolution in discrete-time known as a
convolution sum. Given discrete-time input signals x[n] and h[n], the general expression for
the convolution sum, y[n], is given by the equation,
∑
∞
=−∞
= − k
y[n] x[k]h[n k] (1)
or equivalently ∑
∞
=−∞
= − k
y[n] h[k]x[n k]. That is, the sum is the same if the inputs are
interchanged. While the above applies to signals that are infinite in length, we are concerned
with input signals that are nonzero over a finite interval. Suppose that x[n] has M samples
x[1], x[2],…,x[M] and h[n] has N samples h[1], h[2],…, h[N]. Then output y[n] will have at
most M +N −1 nonzero samples. Here we use time sample 1 as the starting sample rather
than time sample zero to conform with Matlab’s vector indexing. Then Eq. (1) would look
like
∑=
= − +
N
k
y n h k x n k
1
[ ] [ ] [ 1]. (2)
That is, the outputs are:
y[1] = h[1] x[1] + h[2] x[0] + …+ h[N−1] x[3− N ]+ h[N] x[2 − N]
= h[1] x[1]
y[2] = h[1] x[2] + h[2] x[1] + …+ h[N−1] x[4− N ]+ h[N] x[3 − N]
= h[1] x[2] + h[2] x[1]
…
y[n] = h[1] x[n] + h[2] x[n − 1] + …+ h[N−1] x[n +2− N ] + h[N] x[n +1− N ]
…
y[M+N−2] = h[1] x[M+N−2] + h[2] x[M+N−3] + …+ h[N−1] x[M]+ h[N] x[M−1]
= h[N−1] x[M] + h[N] x[M−1]
y[M+N−1] = h[1] x[M+N−1] + h[2] x[M+N−2] + …+ h[N−1] x[M+1]+ h[N] x[M]
= h[N] x[M]
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Although much of your future use of Matlab would mainly require you to run existing
programs and perhaps write scripts to automate this process, it is still important to gain a
more thorough understanding of Matlab from a programming perspective. Another way to
view this is by the old adage,
...give someone a fish and they will be self-sufficient for a day. Teach someone to fish, and
they will be self-sufficient for life...
2. The Task
You are to design, write, debug and test a Matlab function named “convolver” that meets
the following specifications:
• The function is of the form y = convolver(h, x). For general information on how to run a
function, consult Matlab help. In other words, the only inputs are x and h. The sizes of
the input signals, x and h, represented either by row or column vectors, must be
determined by your function. If the input signals are not row or column vectors, the
function must exit with an explanatory error message.
• The user input ”help convolver” will output a one-line help message and then exit.
• It is assumed that the input vectors are indexed from time sample 1, to match Matlab’s
indexing convention. That is, the first nonzero element of vector x is denoted by x(1).
This matches the equations presented in the previous section. It is also assumed that the
first output sample begins at time sample 1.
• In addition to producing the correct output vector, the function should display all three
signals in stem-style subplots in a single figure window. Appropriate axis scaling should
be used to enhance visibility and ease interpretation of the effect of the convolution.
• No Matlab toolbox functions should be used in your code. Only commands from the
basic Matlab language are allowed.
• Your solution should try to conform to Matlab’s array computation language. In other
words, as many computations as possible should be ”vectorized”. That is, matrix/vector
operations should be used wherever possible and the use of loops, although necessary,
should be minimized.
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• In your solution to be handed in, a complete listing of your function should be provided.
Also, the function should be tested with output provided on the following three sample
sets of inputs:
c = convolver (a,b) where:
a=[1 2 3 4] b = [1.5 0.5]
a = [1.5; 0.5] b = [1 2 3 4]
a = [1; 2; 3; 4] b = [1; 1; 1; 1]
This assignment should be completed and the report should be submitted within one week
after completion of the lab. Each team submits one report.