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Journal ArticleDOI

Asymmetric Windows and their Application in Frequency Estimation

01 Dec 2015-Journal of Algorithms & Computational Technology (SAGE PublicationsSage UK: London, England)-Vol. 9, Iss: 4, pp 389-412
TL;DR: The simulation demonstrates that the improved estimation method, in which the symmetric windows are replaced by the asymmetric windows, shows a stronger capability of additive noise resistance than the traditional method.
Abstract: Classic windows have constant time delay and linear phase because of the symmetry and the time shift causality-imposed in the time domain. And thus, all such windows have the same spectral phase response. Removal of the symmetry constraint on a classic window can result in a variable phase response and in an alterable time delay. In essence the time delay becomes shorter will bring about a lot of benefits in speech coding. Some asymmetric windows with better magnitude response also can lead to a better recognition performance if the result is relatively insensitive to phase distortion. However, it is surprising that so little attention has been paid to the asymmetric windows in past literature; and never in past history has this issue been systematically or comprehensively studied. As a result, several methods to obtain the asymmetric windows are being presented in this paper. The asymmetric windows are displayed and compared with the classic windows, concerning both in time and frequency domains. Some ne...
Citations
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Journal ArticleDOI
TL;DR: On the basis of empirical mode decomposition and teager energy operator, the new approach for rolling bearing fault diagnosis based on phase difference correction method is presented in this article, which focuses on...
Abstract: On the basis of empirical mode decomposition and teager energy operator, the new approach for rolling bearing fault diagnosis based on phase difference correction method is presented. It focuses on...

4 citations


Cites methods from "Asymmetric Windows and their Applic..."

  • ...It was first proposed byMcMahon and Barrett,(21) hitherto, three types of PDC methods can be described as: time shifting (TS),(22,23) window length changing(WLC),(24,25) and correction method based on asymmetrical windows (AW).(26,27) TS method needs to choose an appropriate parameter L of time delay....

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Journal ArticleDOI
TL;DR: It was demonstrated that the estimation accuracy under intensive noise can be remarkably improved by using optimizational spectral location strategies, and Macleod’s optimizational strategy is strongly suggested because of its prominent advantage in reducing occurrences of wrong location as well as its best performance in frequency estimation.
Abstract: This paper presented the problem of wrong choice of spectral bins in the energy-based frequency estimation method under intensive noise, and studied its impact on the frequency estimation. Based on the theory of energy-based method, the causes for wrong location of spectral bins in the traditional estimation method were analyzed. In order to reduce wrong choice rate of spectral bins, two optimizational location strategies of spectral bins were introduced, and the effects of them were confirmed by computer simulation. A numerical test under intensive noise was carried out, in which estimation errors returned by optimizational spectral location strategies were compared. It was demonstrated that the estimation accuracy under intensive noise can be remarkably improved by using optimizational spectral location strategies. In particular, Macleod’s optimizational strategy is strongly suggested because of its prominent advantage in reducing occurrences of wrong location as well as its best performance in frequenc...

2 citations

Journal ArticleDOI
Jiufei Luo, Haitao Xu, Kai Zheng, Xinyi Li, Song Feng 
08 Aug 2018-Symmetry
TL;DR: The phase response of windows were further studied, and the phase characteristics of symmetric and asymmetric windows are described, and an improved version of the asymmetric window- based frequency estimation algorithm was proposed.
Abstract: Asymmetric windows are of increasing interest to researchers because of the nonlinear and adjustable phase response, as well as alterable time delay. Short-time phase distortion can provide an essential improvement in speech coding, and also has better performance in speech recognition. The merits of asymmetric windows in the aspect of spectral behaviors have an important function in frequency component detection and parameter estimation. In this paper, the phase response of windows were further studied, and the phase characteristics of symmetric and asymmetric windows are described. The relationship between the barycenter of windows in the time domain, and the phase characteristic at the center of the main lobe in the frequency domain, was established. In light of the relationship, an improved version of the asymmetric window- based frequency estimation algorithm was proposed. The improved algorithm has advantages of straightforward implementation and computational efficiency. The numeric simulation results also indicate that the improved approach is more robust than the traditional method against additive random noise.

1 citations


Cites background or methods from "Asymmetric Windows and their Applic..."

  • ...Sinc all symmetric windows have a const nt time delay T/2, they have the same phase response [2]....

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  • ...In recent years, asymmetric windows have attracted increasing concerns due to the nonlinear and adjustable phase response, as well as alterable time delay [2]....

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  • ...Classic windows have constant time delay and linear phase response due to the symmetry and time shifting causality-imposed in the time domain [2]....

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  • ...The adopted asymmetric windows were [t]2-windows defined in [2], which was constructed by the truncation method....

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  • ...Since all symmetric windows have a constant time delay T/2, they have the same phase response [2]....

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Book ChapterDOI
TL;DR: In this article, a comprehensive review of the past and current work in the field of asymmetric windows is presented, followed by empirical evaluations in the fields of pitch modification, shorter time delay audio processing (e.g., speech coding), frequency analysis, speech processing, and FIR filter design.
Abstract: Symmetric windows are widely used in the field of digital signal processing due to their easy design and linear phase property. Nevertheless, symmetry also implies a few potential drawbacks like longer time delay in short-time frequency analysis and some limitations in frequency response. The removal of the symmetry constraint can therefore lead to asymmetric windows better in certain respects. In signal processing, better signal representations and related improved processing performance can be accomplished. In addition, shorter time delay can be achieved with asymmetric windows. This feature is important for contemporary spoken communications in the Internet or mobile networks and all other real-time signal processing applications. The article gives a comprehensive review of the past and current work in the field of asymmetric windows. We elaborate on our work and related efforts of other researchers inspired by the idea of asymmetry. Shorter time delay and some better spectral properties are the most prominent potential of asymmetric windows. However, there are also some other more subtle properties which can improve the performance in specific application contexts (e.g., frequency estimation and detection of closely spaced components in frequency analysis). Several examples of interesting effects of asymmetric windows are presented, followed by empirical evaluations in the fields of pitch modification, shorter time delay audio processing (e.g., speech coding), frequency analysis, speech processing, and FIR filter design. In addition, a detailed comparison of various asymmetric windows found in the literature to widely known symmetric windows is made taking into account several practical and theoretical aspects. Finally, all presented achievements are summarized in a table which provides a complete overview of the current state of this interesting research and application field.
Proceedings ArticleDOI
01 Oct 2018
TL;DR: In this paper, the authors proposed a hybrid-iteration algorithm to estimate the parameters (frequency and damping factor) of damped exponential signal, which utilizes the phase difference based on asymmetric window as the first implementation and interpolation Discrete Fourier Transform (IpDFT) as the second one.
Abstract: The paper proposed a hybrid-iteration algorithm to estimate the parameters (frequency and damping factor) of damped exponential signal. With regard to core idea of this method, the new algorithm utilizes the phase difference based on asymmetric window as the first implementation and interpolation Discrete Fourier Transform (IpDFT) as the second one. The estimator introduces the asymmetric phase difference method to the decaying case and avoids the error generated from wrong location of spectral line. The root mean squares error (RMSE) was investigated in the case of white Gauss noise to evaluate the capability of robustness against adaptive noise. Extensive numerical simulations show that the RMSEs of the proposed algorithm closely attach to Cramer-Rao lower bound (CRLB). In addition, simulation results also indicate that the new method has excellent performance against random noise compared with other interpolation DFT algorithms.

Cites background or methods from "Asymmetric Windows and their Applic..."

  • ...(21) must exist when k is equal to normalized frequency in the absence of noise [17]....

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  • ...Both characters reveals that the phase difference based on asymmetric method, which was presented by Luo in [17], can also be operated to damped signal....

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  • ...The damped part can be defined as an exponential-decaying-window (EDW), which denotes an asymmetric window as demonstrated in reference [17]....

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  • ...Particularly, the phase slope of EDW with different lengths are equal at the center of main-lobe [16,17]....

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  • ...Where h(·) represents the slope of EDW in frequency domain, which is a complicated function of k and d [17]....

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References
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Journal ArticleDOI
01 Jan 1978
TL;DR: A comprehensive catalog of data windows along with their significant performance parameters from which the different windows can be compared is included, and an example demonstrates the use and value of windows to resolve closely spaced harmonic signals characterized by large differences in amplitude.
Abstract: This paper makes available a concise review of data windows and their affect on the detection of harmonic signals in the presence of broad-band noise, and in the presence of nearby strong harmonic interference. We also call attention to a number of common errors in the application of windows when used with the fast Fourier transform. This paper includes a comprehensive catalog of data windows along with their significant performance parameters from which the different windows can be compared. Finally, an example demonstrates the use and value of windows to resolve closely spaced harmonic signals characterized by large differences in amplitude.

7,130 citations


"Asymmetric Windows and their Applic..." refers background in this paper

  • ...Akhiezer had proposed Cauchy window and Gaussian window[1]....

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  • ...REFERENCE [1] F.J. Harris, On the use of windows for harmonic analysis with the discrete Fourier transform, Proceedings of the IEEE, 66 (1978) 51–83....

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  • ...In Harris’ excellent paper, he summarized some important criteria of the windows in the consideration of harmonic analysis....

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  • ...Thus windowed data is smoothly brought to zero at the boundaries of each period to reduce the discontinuity amplitudes [1]....

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  • ...In 1978, Harris[1] presented his celebrated paper in which a plethora of windows were discussed and compared....

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Book
14 Jul 2012
TL;DR: This account attempts to provide and relate the necessary ideas and techniques in reasonable detail to develop the insight necessary to plan both the acquisition of adequate data and sound procedures for its reduction to meaningful estimates.
Abstract: The measurement of power spectra is a problem of steadily increasing importance which appears to some to be primarily a problem in statistical estimation. Others may see it as a problem of instrumentation, recording and analysis which vitally involves the ideas of transmission theory. Actually, ideas and techniques from both fields are needed. When they are combined, they provide a basis for developing the insight necessary (i) to plan both the acquisition of adequate data and sound procedures for its reduction to meaningful estimates and (ii) to interpret these estimates correctly and usefully. This account attempts to provide and relate the necessary ideas and techniques in reasonable detail — Part I of this article appeared in the January, 1958 issue of THE BELL SYSTEM TECHNICAL JOURNAL.

1,353 citations


"Asymmetric Windows and their Applic..." refers methods in this paper

  • ...Tukey summed up five classic pairs of windows including the rectangle (Dirichlet) window, triangle (Fejer, Bartlet) window, Hanning window, Hamming window and Blackman window[4]....

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Journal ArticleDOI
TL;DR: Correct plots of Harris' windows are presented and additional windows with very good sidelobes and optimal behavior under several different constraints are derived.
Abstract: Some of the windows presented by Harris [1] are not correct in terms of their reported peak sidelobes and optimal behavior. We present corrected plots of Harris' windows and also derive additional windows with very good sidelobes and optimal behavior under several different constraints. The temporal weightings are characterized as a sum of weighted cosines over a finite duration. The plots enable the reader to select a window to suit his requirements, in terms of bias due to nearby sidelobes and bias due to distant sidelobes.

1,024 citations


"Asymmetric Windows and their Applic..." refers background in this paper

  • ...Nuttall [12] derived additional windows with very good sidelobes and optimal behavior under different constraints....

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Book
01 Jan 2009
TL;DR: This paper presents a meta-anatomy of Biomedical Signal Analysis, focusing on the role of ECG waves in the development of central nervous system diseases and their role in the management of disease progression.
Abstract: Dedication. Preface. About the Author. Acknowledgments. Symbols and Abbreviations. 1 Introduction to Biomedical Signals. 1.1 The Nature of Biomedical Signals. 1.2 Examples of Biomedical Signals. 1.3 Objectives of Biomedical Signal Analysis. 1.4 Difficulties in Biomedical Signal Analysis. 1.5 Computer-aided Diagnosis. 1.6 Remarks. 1.7 Study Questions and Problems. 1.8 Laboratory Exercises and Projects. 2 Concurrent, Coupled, and Correlated Processes. 2.1 Problem Statement. 2.2 Illustration of the Problem with Case-studies. 2.3 Application: Segmentation of the PCG. 2.4 Remarks. 2.5 Study Questions and Problems. 2.6 Laboratory Exercises and Projects. 3 Filtering for Removal of Artifacts. 3.1 Problem Statement. 3.2 Illustration of the Problem with Case-studies. 3.3 Time-domain Filters. 3.4 Frequency-domain Filters. 3.5 Optimal Filtering: The Wiener Filter. 3.6 Adaptive Filters for Removal of Interference. 3.7 Selecting an Appropriate Filter. 3.8 Application: Removal of Artifacts in the ECG. 3.9 Application: Maternal - Fetal ECG. 3.10 Application: Muscle-contraction Interference. 3.11 Remarks. 3.12 Study Questions and Problems. 3.13 Laboratory Exercises and Projects. 4 Event Detection. 4.1 Problem Statement. 4.2 Illustration of the Problem with Case-studies. 4.3 Detection of Events and Waves. 4.4 Correlation Analysis of EEG channels. 4.5 Cross-spectral Techniques. 4.6 The Matched Filter. 4.7 Detection of the P Wave. 4.8 Homomorphic Filtering. 4.9 Application: ECG Rhythm Analysis. 4.10 Application: Identification of Heart Sounds. 4.11 Application: Detection of the Aortic Component of S2. 4.12 Remarks. 4.13 Study Questions and Problems. 4.14 Laboratory Exercises and Projects. 5 Waveshape and Waveform Complexity. 5.1 Problem Statement. 5.2 Illustration of the Problem with Case-studies. 5.3 Analysis of Event-related Potentials. 5.4 Morphological Analysis of ECG Waves. 5.5 Envelope Extraction and Analysis. 5.6 Analysis of Activity. 5.7 Application: Normal and Ectopic ECG Beats. 5.8 Application: Analysis of Exercise ECG. 5.9 Application: Analysis of Respiration. 5.10 Application: Correlates of Muscular Contraction. 5.11 Remarks. 5.12 Study Questions and Problems. 5.13 Laboratory Exercises and Projects. 6 Frequency-domain Characterization. 6.1 Problem Statement. 6.2 Illustration of the Problem with Case-studies. 6.3 The Fourier Spectrum. 6.4 Estimation of the Power Spectral Density Function. 6.5 Measures Derived from PSDs. 6.6 Application: Evaluation of Prosthetic Valves. 6.7 Remarks. 6.8 Study Questions and Problems. 6.9 Laboratory Exercises and Projects. 7 Modeling Biomedical Systems. 7.1 Problem Statement. 7.2 Illustration of the Problem. 7.3 Point Processes. 7.4 Parametric System Modeling. 7.5 Autoregressive or All-pole Modeling. 7.6 Pole-zero Modeling. 7.7 Electromechanical Models of Signal Generation. 7.8 Application: Heart-rate Variability. 7.9 Application: Spectral Modeling and Analysis of PCG Signals. 7.10 Application: Coronary Artery Disease. 7.11 Remarks. 7.12 Study Questions and Problems. 7.13 Laboratory Exercises and Projects. 8 Analysis of Nonstationary Signals. 8.1 Problem Statement. 8.2 Illustration of the Problem with Case-studies. 8.3 Time-variant Systems. 8.4 Fixed Segmentation. 8.5 Adaptive Segmentation. 8.6 Use of Adaptive Filters for Segmentation. 8.7 Application: Adaptive Segmentation of EEG Signals. 8.8 Application: Adaptive Segmentation of PCG Signals. 8.9 Application: Time-varying Analysis of Heart-rate Variability. 8.10 Remarks. 8.11 Study Questions and Problems. 8.12 Laboratory Exercises and Projects. 9 Pattern Classification and Diagnostic Decision. 9.1 Problem Statement. 9.2 Illustration of the Problem with Case-studies. 9.3 Pattern Classification. 9.4 Supervised Pattern Classification. 9.5 Unsupervised Pattern Classification. 9.6 Probabilistic Models and Statistical Decision. 9.7 Logistic Regression Analysis. 9.8 The Training and Test Steps. 9.9 Neural Networks. 9.10 Measures of Diagnostic Accuracy and Cost. 9.11 Reliability of Classifiers and Decisions. 9.12 Application: Normal versus Ectopic ECG Beats. 9.13 Application: Detection of Knee-joint Cartilage Pathology. 9.14 Remarks. 9.15 Study Questions and Problems. 9.16 Laboratory Exercises and Projects. References. Index.

674 citations


"Asymmetric Windows and their Applic..." refers methods in this paper

  • ...Recently, windows have been employed to improve the detection of heart rate variability in electrocardiograms [19, 20], to reduce side-lobes of limited diffraction beams by Chebyshev weighting function [21], to aid in the classification of cosmic data[22, 23] and to enhance the reliability of weather prediction models [24]....

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