simple sliding window filter in Matlab

Question

I don't have the package for nlfilter and I didn't quite follow this example.

I have a really simple function fun and I want to apply it to a moving window of an array. The array is Nx1, and I want to look at length k intervals, say. So for N=10 and k=3 and fun = @(x) min(x); I would get

A = [13 14 2 14 10 3 5 9 15 8];

filter(A,k,fun) = [2 2 2 3 3 3 5 8];

Here I only want to look at indices 1,2,3 then 2,3,4 then ... then 8,9,10, so the final sequence is length 7. I can do this easy with a for loop, but I have no idea how to vectorize it for Matlab. Help, please. Thanks.

Answer 1

The post you mentioned gave a general solution for building sliding windows (you could control: overlapping vs. distinct, slide step, overlap amount, windows size)

In your case, it is much simpler and can be easily performed with the HANKEL function:

x = [13 14 2 14 10 3 5 9 15 8];
idx = hankel(1:3, 3:length(x))
min( x(idx) )

---

If you want to build a reusable solution:

function y = myFilter(x,k,fcn)
    idx = hankel(1:k, k:length(x));
    y = cellfun(fcn, num2cell(x(idx),1));
end

which we use as:

x = [13 14 2 14 10 3 5 9 15 8];
y = myFilter(x, 3, @(x)min(x))

Note I am using CELLFUN in case fcn cannot operate across dimensions in a vectorized manner...

Answer 2

Here is one very simple and fast way to do it:

>> min([A(1:(end-2)); A(2:(end-1)); A(3:end)], [], 1)

ans =

     2     2     2     3     3     3     5     8

EDIT: Since you want a full function...

function running_min = running_min(x, k)

xrep = repmat(x, 1, k);
xrep = reshape([xrep zeros(1, k)], length(x)+1, k);
running_min = min(xrep, [], 2)';
running_min = running_min(1:end-k);