In signal processing applications the information about the signal such as frequency (or) period is known a prior for most of the practical signals like ECG, EEG, speech, etc. Inspired by this, in this paper, we propose a new signal representation to estimate the period and frequency information of a given signal with low computational complexity. We achieve this by representing a finite-length discrete-time signal as a linear combination of signals belongs to Ramanujan subspaces. Further, we evaluate the performance of the proposed representation with a simulated example and also by addressing the problem of reducing Power Line Interference (PLI) in an ECG signal. Finally, for a given integer-valued signal, we show that the computational complexity of the proposed transform is quite low in comparison with the existing transforms, and it is quite comparable for a given real (or) complex-valued signal. © 2020 IEEE.

Vijay Kumar Chakka

Electrical Engineering

(SoE) School of Engineering

Shah S.B.

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Shiv Nadar University

Signal Representation Using Ramanujan Subspaces Utilizing A Prior Signal Information

SPCOM 2020 - International Conference on Signal Processing and Communications

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.

Fulltext

IEEE Transactions on Signal Processing

Orthogonal and Non-Orthogonal Signal Representations Using New Transformation Matrices Having NPM Structure

This letter introduces a real valued summation known as complex conjugate pair sum (CCPS). The space spanned by CCPS and its one circular downshift is called complex conjugate subspace (CCS). For a given positive integer N ≥ 3, there exists φ(N)/2 CCPSs forming φ(N)/2 CCSs, where φ(N) is the Euler's totient function. We prove that these CCSs are mutually orthogonal and their direct sum form a φ(N) dimensional subspace sN of ℂN. We propose that any signal of finite length N is represented as a linear combination of elements from a special basis of sd, for each divisor d of N. This defines a new transform named as complex conjugate periodic transform (CCPT). Later, we compared CCPT with discrete Fourier transform (DFT) and Ramanujan periodic transform (RPT). It is shown that, using CCPT, we can estimate the period, hidden periods, and frequency information of a signal. Whereas, RPT does not provide the frequency information. For a complex valued input signal, CCPT offers computational benefit over DFT. A CCPT dictionary based method is proposed to extract non-divisor period information. © 2018 IEEE.

IEEE Signal Processing Letters

A New Signal Representation Using Complex Conjugate Pair Sums

Ramanujan Periodic Transform (RPT) is the newly emerging transform to identify periodicities in the given data. RPT represents the given finite length sequence into a weighted linear combination of signals from Ramanujan subspaces. RPT has the inability of handling the frequency components with in the Ramanujan subspace. This is due to the basis function (Ramanujan sum) used in RPT. To overcome this, a new mixed basis representation is proposed which uses both the sequences from Ramanujan subspace and complex exponentials as basis and both the basis are orthogonal to each other. Using this mixed basis representation, the problem of removing Power Line Interference (PLI) in ECG data is addressed. The methodology is tested on the MIT-BIH Arrhythmia database and the obtained results are competitive when compared with other techniques. © 2017 IEEE.