On pruning the discrete cosine and sine transforms

In the paper it is shown that a limited set of output discrete cosine transform (DCT) samples can be computed by a modified real-valued output-pruned FFT algorithm for appropriately permuted data samples. The same is true for the discrete sine transform (DST). Analogously, when computing data contribution from few DCT or DST samples the input-pruned FFT algorithm for inverse FFT can be applied, the input-pruned algorithms for the inverse DCT or DST are obtained. The algorithms are very efficient, their complexities are O(NlogK), where N is the transform size, and K is a divisor of N equal to or greater than the number of computed transform samples, which is less than the number of computed transform samples, which is less than O(NlogN) for the full DCT or DST algorithm. The algorithms are easy to implement, too.