Orthogonal and Non-Orthogonal Signal Representations Using New Transformation Matrices Having NPM Structure
06 Feb 2020-IEEE Transactions on Signal Processing (Institute of Electrical and Electronics Engineers (IEEE))-Vol. 68, pp 1229-1242
TL;DR: 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).
Abstract: 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).
Citations
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TL;DR: In this article , the authors proposed a Ramanujan Fourier mode decomposition (RFMD) method for gear fault diagnosis, which not only has a complete mathematical theory foundation but also has an excellent ability to identify and extract periodic components.
Abstract: As an important part of rotating machinery, gear is easy to appear some unexpected fault states, and its fault diagnosis is very important. Fourier decomposition method (FDM) is a common method for gear fault diagnosis, but the noise robustness, period recognition, and extraction capabilities of FDM are unsatisfactory. Based on this, in this article, Ramanujan Fourier mode decomposition (RFMD) method is proposed. The RFMD not only has a complete mathematical theory foundation but also has an excellent ability to identify and extract periodic components. Emulational and experimental results of planetary gearbox show that the RFMD method has good noise robustness and can accurately extract gear fault characteristic information. Thus, it is an effective gear fault diagnosis method.
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04 Jun 2021
TL;DR: Evaluation results in terms of accuracy, sensitivity, specificity, and F-score demonstrate that the proposed method is comparable with the state-of-the-art techniques and also robust against artifacts and noise.
Abstract: Epilepsy is a chronic brain disorder that is characterized by intermittent epileptic seizures that can be identified in an electroencephalogram (EEG) signal. This letter proposes a low computational complex method to classify epileptic EEG signals by using a suitable Ramanujan periodic subspace (RPS). Initially, this method divides the given single-channel EEG signal into multiple nonoverlapping EEG blocks, which are projected onto a particular RPS. The energy of the projection is used as a feature to classify each block into epileptic or nonepileptic, using an SVM binary classifier. Here, in order to choose that particular RPS, a few sample blocks from the epileptic (ictal), interictal, and healthy EEG signal are projected onto the divisor RPSs of that block. The difference between the average subspace energy of healthy versus ictal or interictal versus ictal blocks is used as a measure to choose the suitable RPS. Finally, the class of each block of the EEG signal is combined using the majority voting scheme to classify the epileptic EEG signal. A publicly available benchmark EEG database from Bonn University, Germany, is used to evaluate the performance of the proposed method. Furthermore, the EEG signals are added with white Gaussian noise and ocular artifact for testing the robustness of the method against noise. Evaluation results in terms of accuracy, sensitivity, specificity, and F-score demonstrate that the proposed method is comparable with the state-of-the-art techniques and also robust against artifacts and noise.
7 citations
TL;DR: In this article , the affine Ramanujan Fourier transform (ARFT) is combined with affine multiresolution analysis tools for nonstationary signals to provide affine multi-resolution analysis tools.
1 citations
19 Jul 2020
TL;DR: This paper proposes a new signal representation to estimate the period and frequency information of a given signal with low computational complexity by representing a finite-length discrete-time signal as a linear combination of signals belongs to Ramanujan subspaces.
Abstract: 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.
Cites background or methods from "Orthogonal and Non-Orthogonal Signa..."
...It is shown that one of the CCPTs (known as Orthogonal CCPT) has the ability to give divisor period and its corresponding frequency information with less computational complexity over DFT [4], [6]....
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...Based on the type of basis used for Ramanujan subspace like complex exponentials, RSs and both CCPSs((1)) & CCPSs((2)), the corresponding transforms are named as DFT, RPT and Orthogonal CCPT [6] respectively....
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...RPT Mixed Basis (RSs ∪ CCPSs) Mixed Basis (RSs ∪ CEs) OCCPT DFT. • If x(n)∈RN (or) If x(n)∈CN : For these two cases we claim the following relation: RPT = Mixed Basis (RSs ∪ CCPSs) = OCCPT Mixed Basis (RSs ∪ CEs) DFT....
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...Based on the type of basis used for Ramanujan subspace like complex exponentials, RSs and both CCPSs(1) & CCPSs(2), the corresponding transforms are named as DFT, RPT and Orthogonal CCPT [6] respectively....
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...The representations (DFT, RPT, and CCPTs) discussed above are independent of the signal information....
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References
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TL;DR: The newly inaugurated Research Resource for Complex Physiologic Signals (RRSPS) as mentioned in this paper was created under the auspices of the National Center for Research Resources (NCR Resources).
Abstract: —The newly inaugurated Research Resource for Complex Physiologic Signals, which was created under the auspices of the National Center for Research Resources of the National Institutes of He...
11,407 citations
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01 Jan 1989
TL;DR: In this paper, the authors provide a thorough treatment of the fundamental theorems and properties of discrete-time linear systems, filtering, sampling, and discrete time Fourier analysis.
Abstract: For senior/graduate-level courses in Discrete-Time Signal Processing. THE definitive, authoritative text on DSP -- ideal for those with an introductory-level knowledge of signals and systems. Written by prominent, DSP pioneers, it provides thorough treatment of the fundamental theorems and properties of discrete-time linear systems, filtering, sampling, and discrete-time Fourier Analysis. By focusing on the general and universal concepts in discrete-time signal processing, it remains vital and relevant to the new challenges arising in the field --without limiting itself to specific technologies with relatively short life spans.
10,388 citations
8,006 citations
TL;DR: A real-time algorithm that reliably recognizes QRS complexes based upon digital analyses of slope, amplitude, and width of ECG signals and automatically adjusts thresholds and parameters periodically to adapt to such ECG changes as QRS morphology and heart rate.
Abstract: We have developed a real-time algorithm for detection of the QRS complexes of ECG signals. It reliably recognizes QRS complexes based upon digital analyses of slope, amplitude, and width. A special digital bandpass filter reduces false detections caused by the various types of interference present in ECG signals. This filtering permits use of low thresholds, thereby increasing detection sensitivity. The algorithm automatically adjusts thresholds and parameters periodically to adapt to such ECG changes as QRS morphology and heart rate. For the standard 24 h MIT/BIH arrhythmia database, this algorithm correctly detects 99.3 percent of the QRS complexes.
6,686 citations
"Orthogonal and Non-Orthogonal Signa..." refers background or methods in this paper
...Now, a better estimation of R peak locations can be achieved from this filtered signal, using a standard adaptive threshold algorithm [35]....
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...Here the problem of R peak (QRS complex) delineation in an ECG signal is considered, which is important in many ECG based applications [35], [36]....
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Book•
01 Jan 1992TL;DR: This paper presents a meta-analysis of the Z-Transform and its application to the Analysis of LTI Systems, and its properties and applications, as well as some of the algorithms used in this analysis.
Abstract: 1. Introduction. 2. Discrete-Time Signals and Systems. 3. The Z-Transform and Its Application to the Analysis of LTI Systems. 4. Frequency Analysis of Signals and Systems. 5. The Discrete Fourier Transform: Its Properties and Applications. 6. Efficient Computation of the DFT: Fast Fourier Transform Algorithms. 7. Implementation of Discrete-Time Systems. 8. Design of Digital Filters. 9. Sampling and Reconstruction of Signals. 10. Multirate Digital Signal Processing. 11. Linear Prediction and Optimum Linear Filters. 12. Power Spectrum Estimation. Appendix A. Random Signals, Correlation Functions, and Power Spectra. Appendix B. Random Numbers Generators. Appendix C. Tables of Transition Coefficients for the Design of Linear-Phase FIR Filters. Appendix D. List of MATLAB Functions. References and Bibliography. Index.
3,911 citations