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So I'm trying to construct a 2 fold oversampled cosine basis in MATLAB. I know how to construct the basis as a square matrix using the following command:

dct(eye(n,n))

where dct is the discrete cosine transform function and $n\times n$ is the size of my basis but how would I do this if I wanted my basis to be oversampled? Specifically for it to be $n\times 2n$, i.e. a fat matrix such that the columns lose the property of linear independence?

Any help would be greatly appreciated. Thanks in advance!

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    $\begingroup$ Do you have a reference? Can you elaborate on what 2-fold oversampled cosine basis are? $\endgroup$
    – Memming
    Oct 17 '15 at 10:54

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