Time-Frequency Properties of the Short-Time Linear Canonical Transform and Its Application

The short-time linear canonical transform (STLCT), which maps the time domain signal into the joint time and frequency domain, has recently attracted some attention in the area of signal processing. However, its applications are still limited due to the fact that selection of coefficients of the short-time linear canonical series (STLCS) is not unique, because time and frequency elementary functions (together known as basis function) of STLCS do not constitute an orthogonal basis. To solve this problem, this paper investigates a dual window solution. First, the nonorthogonal problem that suffered from original window is fulfilled by orthogonal condition with dual window. Then based on the obtained condition, a dual window computation approach of the GT is extended to the STLCS. In addition, simulations verify the validity of the proposed condition and solutions. Furthermore, some possible applied directions are discussed.

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Sampling theorem for the short-time linear canonical transform and its applications

Signal Processing ◽

10.1016/j.sigpro.2015.01.020 ◽

2015 ◽

Vol 113 ◽

pp. 138-146 ◽

Cited By ~ 17

Author(s):

Zhi-Chao Zhang

Keyword(s):

Sampling Theorem ◽

Linear Canonical Transform ◽

Short Time ◽

Time Linear

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Uncertainty principles for the short-time linear canonical transform of complex signals

Digital Signal Processing ◽

10.1016/j.dsp.2020.102953 ◽

2020 ◽

pp. 102953

Author(s):

Wen-Biao Gao ◽

Bing-Zhao Li

Keyword(s):

Linear Canonical Transform ◽

Uncertainty Principles ◽

Complex Signals ◽

Short Time ◽

Time Linear

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The Wigner-Ville Distribution Based on the Linear Canonical Transform and Its Applications for QFM Signal Parameters Estimation

Journal of Applied Mathematics ◽

10.1155/2014/516457 ◽

2014 ◽

Vol 2014 ◽

pp. 1-8 ◽

Cited By ~ 5

Author(s):

Yu-E Song ◽

Xiao-Yan Zhang ◽

Chun-Heng Shang ◽

Hong-Xia Bu ◽

Xiao-Yan Wang

Keyword(s):

Signal To Noise Ratio ◽

Parameters Estimation ◽

Accurate Estimation ◽

Linear Canonical Transform ◽

Estimation Of Parameters ◽

Position Information ◽

Frequency Distributions ◽

Time Frequency ◽

Definition Of ◽

Short Time

The Wigner-Ville distribution (WVD) based on the linear canonical transform (LCT) (WDL) not only has the advantages of the LCT but also has the good properties of WVD. In this paper, some new and important properties of the WDL are derived, and the relationships between WDL and some other time-frequency distributions are discussed, such as the ambiguity function based on LCT (LCTAF), the short-time Fourier transform (STFT), and the wavelet transform (WT). The WDLs of some signals are also deduced. A novel definition of the WVD based on the LCT and generalized instantaneous autocorrelation function (GWDL) is proposed and its applications in the estimation of parameters for QFM signals are also discussed. The GWDL of the QFM signal generates an impulse and the third-order phase coefficient of QFM signal can be estimated in accordance with the position information of such impulse. The proposed algorithm is fast because it only requires 1-dimensional maximization. Also the new algorithm only has fourth-order nonlinearity thus it has accurate estimation and low signal-to-noise ratio (SNR) threshold. The simulation results are provided to support the theoretical results.

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Strain Sensitivity Enhancement of Broadband Ultrasonic Signals in Plates Using Spectral Phase Filtering

Applied Sciences ◽

10.3390/app11062582 ◽

2021 ◽

Vol 11 (6) ◽

pp. 2582

Author(s):

Lucas M. Martinho ◽

Alan C. Kubrusly ◽

Nicolás Pérez ◽

Jean Pierre von der Weid

Keyword(s):

Fourier Transform ◽

Guided Waves ◽

Strain Level ◽

Energy Concentration ◽

Short Time Fourier Transform ◽

Time Frequency ◽

Frequency Representation ◽

The Fourier Transform ◽

Short Time ◽

Sensitivity Gain

The focused signal obtained by the time-reversal or the cross-correlation techniques of ultrasonic guided waves in plates changes when the medium is subject to strain, which can be used to monitor the medium strain level. In this paper, the sensitivity to strain of cross-correlated signals is enhanced by a post-processing filtering procedure aiming to preserve only strain-sensitive spectrum components. Two different strategies were adopted, based on the phase of either the Fourier transform or the short-time Fourier transform. Both use prior knowledge of the system impulse response at some strain level. The technique was evaluated in an aluminum plate, effectively providing up to twice higher sensitivity to strain. The sensitivity increase depends on a phase threshold parameter used in the filtering process. Its performance was assessed based on the sensitivity gain, the loss of energy concentration capability, and the value of the foreknown strain. Signals synthesized with the time–frequency representation, through the short-time Fourier transform, provided a better tradeoff between sensitivity gain and loss of energy concentration.

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Deep Learning Approach for Vibration Signals Applications

Sensors ◽

10.3390/s21113929 ◽

2021 ◽

Vol 21 (11) ◽

pp. 3929

Author(s):

Han-Yun Chen ◽

Ching-Hung Lee

Keyword(s):

Surface Roughness ◽

Tool Wear ◽

Parameters Optimization ◽

Frequency Spectra ◽

Vibration Signals ◽

Bearing Faults ◽

Time Frequency ◽

And Performance ◽

The One ◽

Short Time

This study discusses convolutional neural networks (CNNs) for vibration signals analysis, including applications in machining surface roughness estimation, bearing faults diagnosis, and tool wear detection. The one-dimensional CNNs (1DCNN) and two-dimensional CNNs (2DCNN) are applied for regression and classification applications using different types of inputs, e.g., raw signals, and time-frequency spectra images by short time Fourier transform. In the application of regression and the estimation of machining surface roughness, the 1DCNN is utilized and the corresponding CNN structure (hyper parameters) optimization is proposed by using uniform experimental design (UED), neural network, multiple regression, and particle swarm optimization. It demonstrates the effectiveness of the proposed approach to obtain a structure with better performance. In applications of classification, bearing faults and tool wear classification are carried out by vibration signals analysis and CNN. Finally, the experimental results are shown to demonstrate the effectiveness and performance of our approach.

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Ultrasonic Assessment of Thickness and Bonding Quality of Coating Layer Based on Short-Time Fourier Transform and Convolutional Neural Networks

Coatings ◽

10.3390/coatings11080909 ◽

2021 ◽

Vol 11 (8) ◽

pp. 909

Author(s):

Azamatjon Kakhramon ugli Malikov ◽

Younho Cho ◽

Young H. Kim ◽

Jeongnam Kim ◽

Junpil Park ◽

...

Keyword(s):

Fourier Transform ◽

Coating Layer ◽

Ultrasonic Pulse ◽

Short Time Fourier Transform ◽

Coating Materials ◽

Time Frequency ◽

High Attenuation ◽

Bonding State ◽

The Time Domain ◽

Short Time

Ultrasonic non-destructive analysis is a promising and effective method for the inspection of protective coating materials. Offshore coating exhibits a high attenuation rate of ultrasonic energy due to the absorption and ultrasonic pulse echo testing becomes difficult due to the small amplitude of the second echo from the back wall of the coating layer. In order to address these problems, an advanced ultrasonic signal analysis has been proposed. An ultrasonic delay line was applied due to the high attenuation of the coating layer. A short-time Fourier transform (STFT) of the waveform was implemented to measure the thickness and state of bonding of coating materials. The thickness of the coating material was estimated by the projection of the STFT into the time-domain. The bonding and debonding of the coating layers were distinguished using the ratio of the STFT magnitude peaks of the two subsequent wave echoes. In addition, the advantage of the STFT-based approach is that it can accurately and quickly estimate the time of flight (TOF) of a signal even at low signal-to-noise ratios. Finally, a convolutional neural network (CNN) was applied to automatically determine the bonding state of the coatings. The time–frequency representation of the waveform was used as the input to the CNN. The experimental results demonstrated that the proposed method automatically determines the bonding state of the coatings with high accuracy. The present approach is more efficient compared to the method of estimating bonding state using attenuation.

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Time–frequency analysis of serum with proton nuclear magnetic resonance for diagnosis of pancreatic cancer

Scientific Reports ◽

10.1038/s41598-020-79087-3 ◽

2020 ◽

Vol 10 (1) ◽

Author(s):

Asahi Sato ◽

Toshihiko Masui ◽

Akitada Yogo ◽

Takashi Ito ◽

Keiko Hirakawa ◽

...

Keyword(s):

Pancreatic Cancer ◽

Carbohydrate Antigen ◽

Serum Markers ◽

Proton Nuclear Magnetic Resonance ◽

Serum Samples ◽

Time Frequency ◽

H Nmr ◽

Free Induction ◽

Short Time ◽

Long Term Survivors

AbstractAlthough serum markers such as carcinoembryonic antigen (CEA) and carbohydrate antigen (CA19-9) have been widely used in screening for pancreatic cancer (PC), their sensitivity and specificity are unsatisfactory. Recently, a novel tool of analyzing serum using the short-time Fourier transform (STFT) of free induction decays (FIDs) obtained by 1H-NMR has been introduced. We for the first time evaluated the utility of this technology as a diagnostic tool for PC. Serum was obtained from PC patients before starting any treatments. Samples taken from individuals with benign diseases or donors for liver transplantation were obtained as controls. Serum samples from both groups underwent 1H-NMR and STFT of FIDs. STFT data were analyzed by partial least squares discriminant analysis (PLS-DA) to clarify whether differences were apparent between groups. As a result, PLS-DA score plots indicated that STFT of FIDs enabled effective classification of groups with and without PC. Additionally, in a subgroup of PC, long-term survivors (≥ 2 years) could be discriminated from short-term survivors (< 2 years), regardless of pathologic stage or CEA or CA19-9 levels. In conclusion, STFT of FIDs obtained from 1H-NMR have a potential to be a diagnostic and prognostic tool of PC.

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