scholarly journals An Efficient Adaptive Window Size Selection Method for Improving Spectrogram Visualization

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Shibli Nisar ◽  
Omar Usman Khan ◽  
Muhammad Tariq
Keyword(s):  
Fourier Transform ◽  
Filter Bank ◽  
Window Size ◽  
Fixed Time ◽  
Frequency Resolution ◽  
High Spectral Resolution ◽  
Background Information ◽  
High Temporal Resolution ◽  
Low Frequencies ◽  
Time Frequency

Short Time Fourier Transform (STFT) is an important technique for the time-frequency analysis of a time varying signal. The basic approach behind it involves the application of a Fast Fourier Transform (FFT) to a signal multiplied with an appropriate window function with fixed resolution. The selection of an appropriate window size is difficult when no background information about the input signal is known. In this paper, a novel empirical model is proposed that adaptively adjusts the window size for a narrow band-signal using spectrum sensing technique. For wide-band signals, where a fixed time-frequency resolution is undesirable, the approach adapts the constant Q transform (CQT). Unlike the STFT, the CQT provides a varying time-frequency resolution. This results in a high spectral resolution at low frequencies and high temporal resolution at high frequencies. In this paper, a simple but effective switching framework is provided between both STFT and CQT. The proposed method also allows for the dynamic construction of a filter bank according to user-defined parameters. This helps in reducing redundant entries in the filter bank. Results obtained from the proposed method not only improve the spectrogram visualization but also reduce the computation cost and achieves 87.71% of the appropriate window length selection.

Spectral decomposition of seismic data with continuous-wavelet transform

Geophysics ◽  
2005 ◽  
Vol 70 (6) ◽  
pp. P19-P25 ◽  
Author(s):  
Satish Sinha ◽  
Partha S. Routh ◽  
Phil D. Anno ◽  
John P. Castagna
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Time Scale ◽  
Fixed Time ◽  
Frequency Resolution ◽  
Continuous Wavelet ◽  
Window Length ◽  
Time Frequency ◽  
Frequency Map

This paper presents a new methodology for computing a time-frequency map for nonstationary signals using the continuous-wavelet transform (CWT). The conventional method of producing a time-frequency map using the short time Fourier transform (STFT) limits time-frequency resolution by a predefined window length. In contrast, the CWT method does not require preselecting a window length and does not have a fixed time-frequency resolution over the time-frequency space. CWT uses dilation and translation of a wavelet to produce a time-scale map. A single scale encompasses a frequency band and is inversely proportional to the time support of the dilated wavelet. Previous workers have converted a time-scale map into a time-frequency map by taking the center frequencies of each scale. We transform the time-scale map by taking the Fourier transform of the inverse CWT to produce a time-frequency map. Thus, a time-scale map is converted into a time-frequency map in which the amplitudes of individual frequencies rather than frequency bands are represented. We refer to such a map as the time-frequency CWT (TFCWT). We validate our approach with a nonstationary synthetic example and compare the results with the STFT and a typical CWT spectrum. Two field examples illustrate that the TFCWT potentially can be used to detect frequency shadows caused by hydrocarbons and to identify subtle stratigraphic features for reservoir characterization.

scholarly journals An Adaptive Resolution Computationally Efficient Short-Time Fourier Transform

2008 ◽  
Vol 2008 ◽  
pp. 1-5 ◽  
Author(s):  
Saeed Mian Qaisar ◽  
Laurent Fesquet ◽  
Marc Renaudin
Keyword(s):  
Fourier Transform ◽  
Input Signal ◽  
Fixed Time ◽  
Frequency Resolution ◽  
Short Time Fourier Transform ◽  
Computationally Efficient ◽  
Time Frequency ◽  
Adaptive Resolution ◽  
Processing Power ◽  
Short Time

The short-time Fourier transform (STFT) is a classical tool, used for characterizing the time varying signals. The limitation of the STFT is its fixed time-frequency resolution. Thus, an enhanced version of the STFT, which is based on the cross-level sampling, is devised. It can adapt the sampling frequency and the window function length by following the input signal local characteristics. Therefore, it provides an adaptive resolution time-frequency representation of the input signal. The computational complexity of the proposed STFT is deduced and compared to the classical one. The results show a significant gain of the computational efficiency and hence of the processing power.

Gaussian Window of Optimal Time-Frequency Resolution in Numerical Implementation of Short-Time Fourier Transform

2011 ◽  
Vol 48-49 ◽  
pp. 555-560 ◽  
Author(s):  
Yang Jin ◽  
Zhi Yong Hao
Keyword(s):  
Fourier Transform ◽  
Continuous Time ◽  
Gaussian Function ◽  
Frequency Resolution ◽  
Optimal Time ◽  
Numerical Implementation ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Gaussian Window ◽  
Short Time

In this paper, we report the condition to keep the optimal time-frequency resolution of the Gaussian window in the numerical implementation of the short-time Fourier transform. Because of truncation and discretization, the time-frequency resolution of the discrete Gaussian window is different from that of the proper Gaussian function. We compared the time-frequency resolution performance of the discrete Gaussian window and Hanning window based on that they have the same continuous-time domain standard deviation, and generalized the condition under which the time-frequency resolution of the Gaussian window will prevail over that of the Hanning window.

The Time-Frequency Resolution of Short Time Fourier Transform Based on Multi-Window Functions

2011 ◽  
Vol 214 ◽  
pp. 122-127 ◽  
Author(s):  
Li Hua Wang ◽  
Qi Dong Zhang ◽  
Yong Hong Zhang ◽  
Kai Zhang
Keyword(s):  
Fourier Transform ◽  
Time Resolution ◽  
High Performance ◽  
Frequency Resolution ◽  
Good Time ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Window Functions ◽  
Short Time ◽  
Good Time Resolution

The short-time Fourier transform has the disadvantage that is does not localize time and frequency phenomena very well. Instead the time-frequency information is scattered which depends on the length of the window. It is not possible to have arbitrarily good time resolution simultaneously with good frequency resolution. In this paper, a new method that uses the short-time Fourier transform based on multi-window functions to enhance time-frequency resolution of signals has been proposed. Simulation and experimental results present the high performance of the proposed method.

Investigation of generalized S-transform analysis windows for time-frequency analysis of seismic reflection data

Geophysics ◽  
2016 ◽  
Vol 81 (3) ◽  
pp. V235-V247 ◽  
Author(s):  
Duan Li ◽  
John Castagna ◽  
Gennady Goloshubin
Keyword(s):  
Temporal Resolution ◽  
Seismic Reflection ◽  
Frequency Resolution ◽  
Low Frequencies ◽  
Seismic Reflection Data ◽  
Time Frequency ◽  
Gaussian Window ◽  
Reflection Data ◽  
S Transform ◽  
Generalized S Transform

The frequency-dependent width of the Gaussian window function used in the S-transform may not be ideal for all applications. In particular, in seismic reflection prospecting, the temporal resolution of the resulting S-transform time-frequency spectrum at low frequencies may not be sufficient for certain seismic interpretation purposes. A simple parameterization of the generalized S-transform overcomes the drawback of poor temporal resolution at low frequencies inherent in the S-transform, at the necessary expense of reduced frequency resolution. This is accomplished by replacing the frequency variable in the Gaussian window with a linear function containing two coefficients that control resolution variation with frequency. The linear coefficients can be directly calculated by selecting desired temporal resolution at two frequencies. The resulting transform conserves energy and is readily invertible by an inverse Fourier transform. This modification of the S-transform, when applied to synthetic and real seismic data, exhibits improved temporal resolution relative to the S-transform and improved resolution control as compared with other generalized S-transform window functions.

scholarly journals A Study of Parameters Setting of the STADZT

10.14311/1654 ◽  
2012 ◽  
Vol 52 (5) ◽  
Author(s):  
Václav Turoň
Keyword(s):  
Spectral Analysis ◽  
Fourier Transform ◽  
Frequency Resolution ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Stationary Signals ◽  
Zolotarev Polynomials ◽  
Non Stationary Signal ◽  
Short Time ◽  
Main Influence

This paper deals with the new time-frequency Short-Time Approximated Discrete Zolotarev Transform (STADZT), which is based on symmetrical Zolotarev polynomials. Due to the special properties of these polynomials, STADZT can be used for spectral analysis of stationary and non-stationary signals with the better time and frequency resolution than the widely used Short-Time Fourier Transform (STFT). This paper describes the parameters of STADZT that have the main influence on its properties and behaviour. The selected parameters include the shape and length of the segmentation window, and the segmentation overlap. Because STADZT is very similar to STFT, the paper includes a comparison of the spectral analysis of a non-stationary signal created by STADZT and by STFT with various settings of the parameters.

scholarly journals Voice Pathology Detection based on Analysis of Modulation Spectrum in Critical Bands

2020 ◽  
Vol 19 (2) ◽  
pp. 249-276
Author(s):  
Maksim Vashkevich ◽  
Ilya Azarov
Keyword(s):  
Filter Bank ◽  
Acoustic Analysis ◽  
Time Window ◽  
Human Perception ◽  
Fixed Time ◽  
Linear Discriminant ◽  
Modulation Spectrum ◽  
Time Frequency ◽  
Frequency Scale ◽  
Voice Signal

The paper presents an approach to the analysis of the modulation spectrum of a voice signal, in which the primary acoustic analysis is performed in bands of unequal width. Nonuniform analysis corresponds to the psychoacoustic laws of human perception of sound information. In the context of the analysis of the modulation spectrum, the considered approach can significantly reduce the resulting number of parameters, which greatly simplifies the task of detecting pathological changes in the voice signal based on the analysis of the parameters of the modulation spectrum. For frequency decomposition of a signal into bands of unequal width, two methods are considered: 1) DFT with channel combination and 2) the use of an nonuniform filter bank. The first method is characterized by a fixed time window for the analysis of all frequency components, while in the second method the time-frequency analysis plan is consistent with the critical frequency scale of the barks. For each method, a practical signal analysis circuit has been developed and described. The paper presents the experimental data on the application of the developed schemes for the analysis of the modulation spectrum to the problem of detecting pathology in a speech signal. The parameters of the modulation spectrum acted as information signs for a classifier built on the basis of linear discriminant analysis. Three different voice bases were used in the experiment (in two cases, the pathology was neurological ALS disease (amyotrophic lateral sclerosis), and in the third case, diseases of the larynx). The parameters of the modulation spectrum obtained in the DFT-based scheme with channel combining turned out to be more preferable for classification with a small number of features, however, greater accuracy (with an increase in the number of features) made it possible to obtain the parameters obtainedin the scheme based on an unequal filter bank. In all cases, the obtained classifiers were highly accurate (more than 97%). The obtained results show that the use of nonuniform time-frequency representation is preferable in the case when the analyzed signal is a sustained vowel phonation, since it provides higher accuracy of pathology detection using fewer modulation parameters

Wavelet-based Segmentation and Feature Extraction of Heart Sounds for Intelligent PDA-based Phonocardiography

2007 ◽  
Vol 46 (02) ◽  
pp. 135-141 ◽  
Author(s):  
H. Nazeran
Keyword(s):  
Feature Extraction ◽  
Spectral Analysis ◽  
Fourier Transform ◽  
Wavelet Transform ◽  
Digital Signal ◽  
Heart Sounds ◽  
Segmentation Algorithm ◽  
Frequency Resolution ◽  
Time Frequency ◽  
Frequency Information

Summary Objectives : Many pathological conditions of the cardiovascular system cause murmurs and aberrations in heart sounds. Phonocardiography provides the clinician with a complementary tool to record the heart sounds heard during auscultation. The advancement of intracardiac phonocardiography combined with modern digital signal processing techniques has strongly renewed researchers' interest in studying heart sounds and murmurs.The aim of this work is to investigate the applicability of different spectral analysis methods to heart sound signals and explore their suitability for PDA-based implementation. Methods : Fourier transform (FT), short-time Fourier transform (STFT) and wavelet transform (WT) are used to perform spectral analysis on heart sounds. A segmentation algorithm based on Shannon energy is used to differentiate between first and second heartsounds. Then wavelet transform is deployed again to extract 64 features of heart sounds. Results : The FT provides valuable frequency information but the timing information is lost during the transformation process. The STFT or spectrogram provides valuable time-frequency information but there is a trade-off between time and frequency resolution. Waveletanalysis, however, does not suffer from limitations of the STFT and provides adequate time and frequency resolution to accurately characterize the normal and pathological heartsounds. Conclusions : The results show that the wavelet-based segmentation algorithm is quite effective in localizing the important components of both normal and abnormal heart sounds. They also demonstrate that wavelet-based feature extraction provides suitable feature vectors which are clearly differentiable and useful for automatic classification of heart sounds.

Seismic spectral decomposition using deconvolutive short-time Fourier transform spectrogram

Geophysics ◽  
2013 ◽  
Vol 78 (2) ◽  
pp. V43-V51 ◽  
Author(s):  
Wenkai Lu ◽  
Fangyu Li
Keyword(s):  
Fourier Transform ◽  
Spectral Decomposition ◽  
Reservoir Characterization ◽  
Low Frequency ◽  
Seismic Signal ◽  
Frequency Resolution ◽  
Short Time Fourier Transform ◽  
Distribution Method ◽  
Time Frequency ◽  
Short Time

The spectral decomposition technique plays an important role in reservoir characterization, for which the time-frequency distribution method is essential. The deconvolutive short-time Fourier transform (DSTFT) method achieves a superior time-frequency resolution by applying a 2D deconvolution operation on the short-time Fourier transform (STFT) spectrogram. For seismic spectral decomposition, to reduce the computation burden caused by the 2D deconvolution operation in the DSTFT, the 2D STFT spectrogram is cropped into a smaller area, which includes the positive frequencies fallen in the seismic signal bandwidth only. In general, because the low-frequency components of a seismic signal are dominant, the removal of the negative frequencies may introduce a sharp edge at the zero frequency, which would produce artifacts in the DSTFT spectrogram. To avoid this problem, we used the analytic signal, which is obtained by applying the Hilbert transform on the original real seismic signal, to calculate the STFT spectrogram in our method. Synthetic and real seismic data examples were evaluated to demonstrate the performance of the proposed method.

scholarly journals Efficient Rotational Angular Velocity Estimation of Rotor Target via Modified Short-Time Fractional Fourier Transform

2021 ◽  
Vol 13 (10) ◽  
pp. 1970
Author(s):  
Wantian Wang ◽  
Yong Zhu ◽  
Ziyue Tang ◽  
Yichang Chen ◽  
Zhenbo Zhu ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Angular Velocity ◽  
Frequency Spectrum ◽  
Hough Transform ◽  
Fractional Fourier Transform ◽  
Velocity Estimation ◽  
Frequency Resolution ◽  
Time Frequency ◽  
Angular Velocity Estimation ◽  
Short Time

As a special micro-motion feature of rotor target, rotational angular velocity can provide a discriminant basis for target classification and recognition. In this paper, the authors focus on an efficient rotational angular velocity estimation method of the rotor target is based on the combination of the time–frequency analysis algorithm and Hough transform. In order to avoid the problems of low time–frequency resolution and cross-term interference in short-time Fourier transform and Wigner–Ville distribution algorithm, a modified short-time fractional Fourier transform (M-STFRFT) is proposed to obtain the time-FRFT domain (FRFD)-frequency spectrum with the highest time–FRFD–frequency resolution. In particular, an orthogonal matching pursuit (OMP)-based algorithm is proposed to reduce the computational complexity when estimating the matched transform order in the proposed M-STFRFT algorithm. Firstly, partial transform order candidates are selected randomly from the complete candidates. Then, a partial entropy vector corresponding to partial transform order candidates is calculated from the FRFT results and utilized to reconstruct the complete entropy vector via the OMP algorithm, and the matched transform order can be estimated by searching minimum entropy. Based on the estimated matched transform order, STFRFT is performed to obtain the time–FRFD–frequency spectrum. Moreover, Hough transform is employed to obtain the energy accumulation spectrum, and the micro-Doppler parameter of rotational angular velocity can be estimated by searching the peak value from the energy accumulation spectrum. Both simulated data and measured data collected by frequency modulated continuous wave radar validate the effectiveness of the proposed algorithm.

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