## Fast algorithms for the discrete cosine transform.(English)Zbl 0762.65103

Authors’ summary: We introduce several fast algorithms for computing discrete cosine transforms (DCT’s) and their inverses on multidimensional inputs of sizes which are powers of 2. Because the one-dimensional 8- point DCT and the two-dimensional $$8\times 8$$-point DCT are so widely used, we discuss them in detail. We also present algorithms for computing scaled DCT’s and their inverses; these have applications in compression of continuous tone image data, where the DCT is generally followed by scaling and quantization.

### MSC:

 65T50 Numerical methods for discrete and fast Fourier transforms
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