I am doing a research project for DST (Discrete Sine Transform) versus DCT (Discrete Cosine Transform) image compression and for my conclusion, my supervisor told me to discuss why the differences occur, I am not entirely sure how to explain the reasons why the coefficients are spread in a specific way.

Any idea why they differ so much for coefficients?

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    $\begingroup$ So, if you are not entirely sure how to explain, which can be understood, what are your partial guesses? $\endgroup$ – Laurent Duval Jan 27 '18 at 16:45
  • $\begingroup$ @LaurentDuval I understand that a lot of the difference comes from the fact that sin(0) is shifted more than cos(0) and cos(0) essentially allows us to have the DC being the average of all the other values which makes it better, but that's the extent to which i understand the issue, any other further help is much appreciated $\endgroup$ – InsertRealName Jan 29 '18 at 19:24

A DCT is roughly equivalent to a DFT of a vector after it is doubled by mirroring by a symmetric reflection. This produces FFT input that does not have a discontinuity either in the middle or circularly. A DST is roughly equivalent to a DFT after an antisymmetric mirrored extension. This antisymmetric addition can easily result in discontinuities both in the middle and around the circle. Discontinuities are represented by energy in the high frequency bins in the FFT results. These high frequency artifacts are usually undesirable when using a transform for compression.

Since the DCT does not have this potential high frequency content due to circular discontinuities (as does a DST or FFT), the same total energy is thus spread lower in frequency, which potentially allows for greater compression of the high frequency DCT bins, while remaining below some visible threshold.

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