Fast Radix- $q$ and Mixed-Radix Algorithms for Type-IV DCT

摘要

This letter proposes a fast radix-$q$ algorithm to compute type-IV discrete cosine transform (DCT) of the length $q ^{lambda}$, where $q$ is an odd positive integer. The proposed fast radix- $q$ algorithm has merits in computational complexity, parallelism, and numerical stability over existing algorithms. Furthermore, the fast radix-$q$ algorithm is used to develop the fast mixed-radix type-II/type-IV DCT algorithm for composite lengths.