Multiplier-less discrete sinusoidal and lapped transforms using sum-of-powers-of-two (SOPOT) coefficients

Abstract

This paper proposes a new family of multiplier-less discrete cosine and sine transforms called the SOPOT DCTs and DSTs. The fast algorithm of Wang [10] is used to parameterize all the DCTs and DSTs in terms of certain (2×2) matrices, which are then converted to SOPOT representation using a method previously proposed by the authors [7]. The forward and inverse transforms can be implemented with the same set of SOPOT coefficients. A random search algorithm is also proposed to search for these SOPOT coefficients. Experimental results show that the (2×2) basic matrix can be implemented, on the average, in 6 to 12 additions. The proposed algorithms therefore require only O(N log2N) additions, which is very attractive for VLSI implementation. Using these SOPOT DCTs/DSTs, a family of SOPOT Lapped Transforms (LT) is also developed. They have similar coding gains but much lower complexity than their real-valued counterparts.