Efficient Recursive Algorithm for Discrete Cosine Transform and Inverse Discrete Cosine Transform

Abstract

In this paper, efficient algorithms based on recursive technique are proposed for even length Discrete cosine Transform (DCT) and Inverse Discrete Cosine Transform (IDCT). The recursive relations are derived to compute N-point DCT and IDCT coefficients by utilizing $\frac {N}{1}$execution cycles per transform coefficient. Reduction in execution cycle from $N$in general length structures to $\frac {N}{1}$in suggested algorithm reduces the computation time as well as the number of real multiplications and addition operations required to compute DCT/IDCT. These recursive relations are realized by generic Infinite impulse response filter structures. Presented IIR-Filter structures for DCT and IDCT are compared with previously existing DCT/ IDCT recursive structure in the literature and it can be concluded that the proposed structures are more hardware and computationally efficient than most of them. The realized recursive structures are simple, modular, regular, and are suitable for VLSI implementation.