Fast computation of transform coefficients for a subadjacent block for a transform family

The authors examine several different kinds of subadjacent blocks, and consider fast computation for a transform family including the Walsh-Hadamard transform and the Rh transform as special cases. The approach proposed here provides a direct frequency-frequency procedure. Results indicate that, for this transform family, a reduction of the number of multiplications and additions is achieved by a factor of two-thirds. An example for the Rh transform shows that further reduction of arithmetic operations is also possible. The results of this method are even better for the Walsh-Hadamard transform. The new algorithms can reduce the number of additions from the level O(N log ₂ N) to the level O(N), as compared to the traditional method