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:
$\mbox{dct(eye($n,n$))}$
where dct is the discrete cosine transform function and nxn 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 $n\times2n$, i.e. a fat matrix such that the columns lose the property of linear independence?
Any help would be greatly appreciated. Thanks in advance!
Simply zeropad the array prior to taking the DCT. Just make sure that the zeros are placed at the higher frequencies.