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Fast algorithms for computing the DHT of short transform lengths (N = 2, 3, 4, 5, 7, 8, 9 and 16) are derived. A new prime-factor algorithm is also proposed to compute the long-length DHTs from the short-length DHT algorithms. The short-length algorithms (except for N = 8 and N = 16) are such that the even and the odd parts of the DHT components are obtained directly, without any additional computation. This feature of the short-length algorithms makes the proposed prime-factor DHT algorithmdoi:10.1049/ip-f-2.1993.0009 fatcat:7yos6qmqvfbyro5gih56hf3xoa