A discrete cosine transform (DCT)
2016-08-23
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A discrete cosine transform (DCT) expresses a finite sequence of data points in terms of a sum of cosine
functions oscillating at different frequencies. DCTs are important to numerous applications in science and
engineering, from lossy compression of audio (e.g. MP3) and images (e.g. JPEG) (where small high-frequency
components can be discarded), to spectral methods for the numerical solution of partial differential equations.
The use of cosine rather than sine functions is critical in these applications: for compression, it turns out that
cosine functions are much more efficient (as described below, fewer functions are needed to approximate a
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