Unified Recursive Structure for Forward and Inverse Modified DCT/DST/DHT

Abstract

This paper proposes implementation of the Modified Discrete Sine Transform (MDST) and Inverse MDST (IMDST) using recursive structures. The formulae required for recursive structures have been derived. Discrete Hartley Transform (DHT), a real-valued transform, is closely related to Discrete Fourier Transform (DFT) of a real-valued sequence and hence its use as an alternative to the Fourier Transform avoids complex arithmetic. This paper presents Modified Discrete Hartley Transform (MDHT)/Inverse MDHT (IMDHT) using Modified Discrete Cosine Transform (MDCT)/ Inverse MDCT (IMDCT) and MDST/Inverse MDST (IMDST) recursive structures. The proposed structures are used for simultaneous computation of MDCT/MDST/MDHT of length N (divisible by four) and their Inverse (IMDST/IMDHT). The proposed structures are parallel, simple, regular and therefore highly suitable for VLSI implementation.