Block diagonal structure in discrete transforms

The author investigates and summarises some of the computational tasks of discrete transforms in which block diagonal structure plays a dominant role. Walsh-Hadamard transform (WHT) based algorithm designs for various well known discrete transforms are presented; it can be proved that, owing to their block diagonal structure, the WHT based discrete transforms are more efficient than those of the conventional radix-r algorithms for transforms of length N\n\n\t\t