Can someone (maybe @hotpaw?) Explain How to use a size N complex DFT to compute a size N/2 real DCT?

Also, I noticed that the DCT matrix (which can be obtained in Matlab by dctmtx(n)) contains dct basis vectors that are not whole (integer) frequency numbers e.g. the second basis vector is only 1 half of a cycle (0.5 Hz). Why is that so?

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    $\begingroup$ that's already answered before, please search the site... $\endgroup$ – Fat32 Jul 19 '19 at 19:31
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    $\begingroup$ write DCT by FFT on the search bar to get your results... $\endgroup$ – Fat32 Jul 19 '19 at 19:50

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