Header menu link for other important links
Orthogonal and Non-Orthogonal Signal Representations Using New Transformation Matrices Having NPM Structure
Shah S.B., , Reddy A.S.
Published in Institute of Electrical and Electronics Engineers Inc.
Volume: 68
Pages: 1229 - 1242
In this article, we introduce two types of real-valued sums known as Complex Conjugate Pair Sums (CCPSs) denoted as CCPS^{(1)} and CCPS^{(2)}, and discuss a few of their properties. Using each type of CCPSs and their circular shifts, we construct two non-orthogonal Nested Periodic Matrices (NPMs). As NPMs are non-singular, this introduces two non-orthogonal transforms known as Complex Conjugate Periodic Transforms (CCPTs) denoted as CCPT^{(1)} and CCPT^{(2)}. We propose another NPM, which uses both types of CCPSs such that its columns are mutually orthogonal, this transform is known as Orthogonal CCPT (OCCPT). After a brief study of a few OCCPT properties like periodicity, circular shift, etc., we present two different interpretations of it. Further, we propose a Decimation-In-Time (DIT) based fast computation algorithm for OCCPT (termed as FOCCPT), whenever the length of the signal is equal to 2^v, v in mathbb {N}. The proposed sums and transforms are inspired by Ramanujan sums and Ramanujan Period Transform (RPT). Finally, we show that the period (both divisor and non-divisor) and frequency information of a signal can be estimated using the proposed transforms with a significant reduction in the computational complexity over Discrete Fourier Transform (DFT). © 1991-2012 IEEE.
About the journal
Published in Institute of Electrical and Electronics Engineers Inc.
Open Access
Impact factor