ON THE COMPUTATION OF RUNNING DISCRETE COSINE AND SINE TRANSFORMS

There exist some situations in signal processing where it is necessary to compute in real time, the transform coefficients of a set of N time domain samples in a block that gets updated continuously with the arrival of a new sample. A familiar example is the frequency domain implementation of a tapped delay line (TDL) adaptive filter. One method of computing the updated (running or instantaneous) transform coefficients without resorting to the computation of N point transform each time the block gets updated, is to use the shift property of the transform. For the computation of the updated discrete cosine transform-II (DCT-II), discrete sine transform-II (DST-II), discrete cosine transform-IV (DCT-IV), and discrete sine transform-IV (DST-IV) as defined in [5], usage of the shift property requires simultaneous computation (if not available as a by-product of the desired transform computation process) and updating of corresponding DST-II, DCT-II, DST-IV, and DCT-IV, respectively. This requirement of an additional transform computation and (or) updating, results in an increased computational burden. In this paper, we give an alternate algorithm for computing updated transform coefficients for DCT-II, DST-II, DCT-IV, and DST-IV that is computationally attractive for real-time implementation. An architecture for the VLSI implementation of the proposed algorithms is also given.