Discrete sine transform and its inverse—realization through recursive algorithms

Abstract

SUMMARYIn this paper, the implementation of the discrete sine transform (DST) and its inverse (IDST) are developed. General length structure of the DST and IDST, which can be implemented by using the recursive structures, has been proposed. Necessary formulas required for the recursive structures have been derived using mathematical manipulations.

Regressive Structures for Computation of DST-II and Its Inverse

“…Both of the algorithms compute the DST/IDST of an N point real sequence. Although the proposed algorithm does not optimize the number of computational cycle, but has advantage in terms of hardware compared to previous approach [14]. Further, the filter structure is numerically stable, as it involves no division at all.…”

“…In Table 1 the number of multipliers, adders and latches required by the present algorithm is compared with those required in algorithms [14]. It can be seen from Table 1 that the new recursive algorithm is efficient in terms of saving the number of multipliers, adder, and latches compared to algorithm [14]. Both of the algorithms compute the DST/IDST of an N point real sequence.…”

“…Further, the filter structure is numerically stable, as it involves no division at all. Algorithm [14] needs addition and subtraction of input sequence whereas the input sequence for the present algorithm is in the natural order, which makes the proposed approach suitable for on-line computation. Table 2 shows the comparison of computational complexity of the proposed algorithm with the other algorithms [15][16][17][18].…”

“…Chiang and Liu [13] suggested a regressive structure for DCT-IV and DST-IV using second order digital filters. This paper is aimed at developing a similar regressive filter structure for DST-II/IDST-II that provides considerable hardware saving compared to the existing algorithm [14] and also reduces the computation complexity in terms of number of operation (multiplication and addition) as compared to the existing algorithms [15][16][17][18]. The advantage of this implementation is that no permutation is required for the input/output sequences, and therefore it is especially suitable for on-line computation.…”

“…The proposed algorithm not only minimizes the arithmetic complexity compared to the existing algorithms (Wany (1990), Hupta and Rao (1990), Yip and Rao (1987), Murthy and Swamy (1992)) but also provides hardware savings over the algorithm (Jain et al (2008)) by the same authors. The naturally ordered input sequence makes the new algorithms suitable for on-line computation.…”