Low-complexity digital filter structures and characteristics using orthogonal transforms

This paper discusses recursive implementation of sinusoidal discrete orthogonal transforms which allow the transform coefficients to be updated each clock cycle. Recursive filters designed through the discrete Hartley, cosine and sine transforms (DHT, DCT and DST respectively) are used for the discussions. Low-complexity structures, the number of delays, multipliers and adders required are given and discussed in detail. We show that the designs involving the DCT and DST manifest a coupling which, when removed, gives DCT, DST and DHT filters efficiently via one design procedure. We also show how the DHT filters are generated by summing the outputs of DCT and DST filters