3
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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?

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  • $\begingroup$ Why don't you use filter instead? Something like filter([1 2 1],1,x) $\endgroup$ – Juancho Jul 5 '12 at 16:24
  • $\begingroup$ Convolve seems a good candidate, too... $\endgroup$ – heltonbiker Jul 5 '12 at 18:24
5
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You could do the following-

kernel = [1 2 1];
s = conv2(eye(numMeasurements), kernel, 'same')
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  • $\begingroup$ Thanks Jim. That works fine, but is there not some matrix operation: S=operation(eye(n,n),kernel) ? $\endgroup$ – Andy Jul 5 '12 at 16:46
  • $\begingroup$ Not that I'm aware of. $\endgroup$ – Jim Clay Jul 5 '12 at 16:50
  • $\begingroup$ @Andy Changed the solution to make it much more compact and more like you want, I think. $\endgroup$ – Jim Clay Jul 5 '12 at 20:23
  • $\begingroup$ Thanks Jim! Something like that was exactly what I was looking for. $\endgroup$ – Andy Jul 6 '12 at 10:53
  • $\begingroup$ 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. $\endgroup$ – wrapperapps Jul 6 '12 at 13:27

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