In Matlab: how do I quickly create smoothing matrices?

Question

Say I have 5 measurements of a signal as a column vector: x. I can smooth the signal by multiplying it with a smoothing matrix:

$\ \mathbf{xs=S*x} $

For instance I might use [1 2 1] as a smoothing kernel in which case I get:

S =
     2     1     0     0     0
     1     2     1     0     0
     0     1     2     1     0
     0     0     1     2     1
     0     0     0     1     2

So far I have been using the function sparse() to build the matrix diagonal by diagonal, but this quickly becomes tedious.

How can I quickly create a mxm smoothing matrix from a 1xn convolution kernel in Matlab?

Why don't you use filter instead? Something like filter([1 2 1],1,x) — Juancho, Jul 05 '12 at 16:24

Jim Clay · Accepted Answer · 2012-07-05T20:22:30.880

5

You could do the following-

kernel = [1 2 1];
s = conv2(eye(numMeasurements), kernel, 'same')

edited Jul 05 '12 at 20:22

answered Jul 05 '12 at 16:32

Jim Clay

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Thanks Jim. That works fine, but is there not some matrix operation: S=operation(eye(n,n),kernel) ? – Andy Jul 05 '12 at 16:46
Not that I'm aware of. – Jim Clay Jul 05 '12 at 16:50
@Andy Changed the solution to make it much more compact and more like you want, I think. – Jim Clay Jul 05 '12 at 20:23
Thanks Jim! Something like that was exactly what I was looking for. – Andy Jul 06 '12 at 10:53
Sorry I can't comment yet, but just in case you didn't know, you could define a function in another .m file and use it like your suggested "S=operation(eye(n,n),kernel)" if that's what you really want. – wrapperapps Jul 06 '12 at 13:27
@wrapperapps Comment converted :) – datageist Jul 06 '12 at 13:37

In Matlab: how do I quickly create smoothing matrices?

1 Answers1