Implement a function that calculates 1D Discrete Cosine Transform (DCT-II) for each row of a given input matrix so that the outputs are in columns.
For example:
Input:
[1 0 0 0]
Gives:
mydct([1 0 0 0])
ans =
0.5
0.65328
0.5
0.2706
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A fair warning to the challenger: the requested DCT-II is the orthogonal version, which means it needs to be multiplied by sqrt(2/N) where N is the size of the row, and the first element of the DCT x0 needs to be multiplied by 1/sqrt(2). It took me a while to understand. Wikipedia's formula is almost right, but it is missing those terms, which are mentioned only further below. Look at MATLAB's documentation (DCT-2), https://www.mathworks.com/help/signal/ref/dct.html, to find the proper formula.