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Orthogonal and Non-Orthogonal Signal Representations Using New Transformation Matrices Having NPM Structure
- Publication Year :
- 2021
-
Abstract
- In this paper, 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).<br />13 pages, 5 figures
- Subjects :
- Signal Processing (eess.SP)
FOS: Computer and information sciences
Complex conjugate
Divisor
Information Theory (cs.IT)
Computer Science - Information Theory
020206 networking & telecommunications
02 engineering and technology
Type (model theory)
Circular shift
Ramanujan's sum
Combinatorics
symbols.namesake
Discrete Fourier transform (general)
Transformation matrix
Signal Processing
FOS: Electrical engineering, electronic engineering, information engineering
0202 electrical engineering, electronic engineering, information engineering
Euler's formula
symbols
Electrical and Electronic Engineering
Electrical Engineering and Systems Science - Signal Processing
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....159c4a12d512e0a21a43e59f879b9ecc