A review of time–frequency representations, with application to sound/music analysis–resynthesis

1997 ◽  
Vol 2 (3) ◽  
pp. 193-205 ◽  
Author(s):  
PAUL MASRI ◽  
ANDREW BATEMAN ◽  
NISHAN CANAGARAJAH
Keyword(s):  
Music Analysis ◽  
Intermediate Representation ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Time Domain Signal ◽  
Analysis Process ◽  
Frequency Representation ◽  
The Time Domain ◽  
Higher Order Spectra ◽  
Short Time

Analysis–resynthesis (A–R) systems gain their flexibility for creative transformation of sound by representing sound as a set of musically useful features. The analysis process extracts these features from the time domain signal by means of a time–frequency representation (TFR). The TFR provides an intermediate representation of sound that must make the features accessible and measurable to the rest of the analysis. Until very recently, the short-time Fourier transform (STFT) has been the obvious choice for time–frequency representation, despite its limitations in terms of resolution. Recent and ongoing developments are providing several alternative schemes that allow for a more considered choice of TFR. This paper reviews these contemporary approaches in comparison with the more classical ones and with reference to their applicability, merits and shortcomings for application to sound analysis. (Where they have been successfully applied, details are provided.) The techniques reviewed include linear, bilinear and higher-order spectra, nonparametric and parametric methods and some sound-model-specific TFRs.

The importance of the time–frequency representation for sound/music analysis–resynthesis

1997 ◽  
Vol 2 (3) ◽  
pp. 207-214
Author(s):  
PAUL MASRI ◽  
ANDREW BATEMAN ◽  
NISHAN CANAGARAJAH
Keyword(s):  
System Design ◽  
Time Domain ◽  
Music Analysis ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Time Domain Signal ◽  
Frequency Representation ◽  
Initial Stage ◽  
Original Time ◽  
Short Time

The time–frequency representation (TFR) is the initial stage of analysis in sound/music analysis–resynthesis (A–R) systems. Given a time-domain waveform, the TFR makes temporal and spectral detail available to the remainder of the analysis, so that the component features may be extracted. The resulting ‘feature set’ must represent the sound as completely as the original time-domain signal, if the A–R system is to be capable of effective transformation and good synthesis sound quality. Therefore the system as a whole is reliant upon the TFR to make the sound components detectable, separable and measurable. Yet the standard TFR to-date is the short-time Fourier transform (STFT), of which the shortcomings, in terms of resolution, are well recognised. The purpose of this paper is to demonstrate the importance of the TFR to system function and system design. Poor feature extraction is shown to result from the use of inappropriate TFRs, whose underlying assumptions and expectations do not match those of the system. Existing models are used as case studies, with examples of performance for different sound types. A philosophy for A–R system design that includes TFR design is presented and a methodology for implementing it is proposed.

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

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.

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

Coatings ◽  
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.

scholarly journals Time-frequency Analysis of Multicomponent LFM signal based on Hough and Chirplet Transform

2018 ◽  
Vol 173 ◽  
pp. 03054
Author(s):  
Xueqin Zhang ◽  
Ruolun Liu
Keyword(s):  
Fourier Transform ◽  
Line Detection ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Frequency Representation ◽  
Chirplet Transform ◽  
Frequency Map ◽  
Linear Frequency Modulated Signal ◽  
Short Time

The Chirplet Transform (CT) is effective in the characterization of IF for mono-component linear-frequency-modulated signal. However, During the initialization process, using the peak of the time-frequency map of the short-time Fourier transform to fit the line is greatly affected by noise. For the multi-component signals, it is more difficult to distinguish and fit different IF lines. Since the Hough is good at a common algorithm for the line detection, the ridge edge fitting is replaced by the Hough transform in this paper. The experiment results show significant improvement in the obtained time-frequency representation.

scholarly journals Applications of an Improved Time-Frequency Filtering Algorithm to Signal Reconstruction

2017 ◽  
Vol 2017 ◽  
pp. 1-14 ◽  
Author(s):  
Junbo Long ◽  
Haibin Wang ◽  
Daifeng Zha ◽  
Hongshe Fan ◽  
Zefeng Lao ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Stable Distribution ◽  
Signal Reconstruction ◽  
Order Moment ◽  
Frequency Filtering ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Noise Environment ◽  
Frequency Representation ◽  
Short Time

The short time Fourier transform time-frequency representation (STFT-TFR) method degenerates, and the corresponding short time Fourier transform time-frequency filtering (STFT-TFF) method fails underαstable distribution noise environment. A fractional low order short time Fourier transform (FLOSTFT) which takes advantage of fractionalporder moment is proposed forαstable distribution noise environment, and the corresponding FLOSTFT time-frequency representation (FLOSTFT-TFR) algorithm is presented in this paper. We study vector formulation of the FLOSTFT and inverse FLOSTFT (IFLOSTFT) methods and propose a FLOSTFT time-frequency filtering (FLOSTFT-TFF) method which takes advantage of time-frequency localized spectra of the signal in time-frequency domain. The simulation results show that, employing the FLOSTFT-TFR method and the FLOSTFT-TFF method with an adaptive weight function, time-frequency distribution of the signals can be better gotten and time-frequency localized region of the signal can be effectively extracted fromαstable distribution noise, and also the original signal can be restored employing the IFLOSTFT method. Their performances are better than the STFT-TFR and STFT-TFF methods, and MSEs are smaller in differentαand GSNR cases. Finally, we apply the FLOSTFT-TFR and FLOSTFT-TFF methods to extract fault features of the bearing outer race fault signal and restore the original fault signal fromαstable distribution noise; the experimental results illustrate their performances.

scholarly journals Sampled and discretized of short-time Fourier transform and non-negative matrix factorization: the single-channel source separation case

2020 ◽  
Vol 9 (1) ◽  
pp. 41-48
Author(s):  
Jans Hendry ◽  
Isnan Nur Rifai ◽  
Yoga Mileniandi
Keyword(s):  
Fourier Transform ◽  
Matrix Factorization ◽  
Single Channel ◽  
Source Separation ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Frequency Representation ◽  
Short Time ◽  
Better Than ◽  
Non Negative Matrix Factorization

The Short-time Fourier transform (STFT) is a popular time-frequency representation in many source separation problems. In this work, the sampled and discretized version of Discrete Gabor Transform (DGT) is proposed to replace STFT within the single-channel source separation problem of the Non-negative Matrix Factorization (NMF) framework. The result shows that NMF-DGT is better than NMF-STFT according to Signal-to-Interference Ratio (SIR), Signal-to-Artifact Ratio (SAR), and Signal-to-Distortion Ratio (SDR). In the supervised scheme, NMF-DGT has a SIR of 18.60 dB compared to 16.24 dB in NMF-STFT, SAR of 13.77 dB to 13.69 dB, and SDR of 12.45 dB to 11.16 dB. In the unsupervised scheme, NMF-DGT has a SIR of 0.40 dB compared to 0.27 dB by NMF-STFT, SAR of -10.21 dB to -10.36 dB, and SDR of -15.01 dB to -15.23 dB.

An Adaptive Time–Frequency Representation and its Fast Implementation

2006 ◽  
Vol 129 (2) ◽  
pp. 169-178 ◽  
Author(s):  
Bao Liu ◽  
Sherman Riemenschneider ◽  
Zuowei Shen
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Frequency Analysis ◽  
Continuous Wavelet Transform ◽  
Continuous Wavelet ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Frequency Representation ◽  
Adaptive Time ◽  
Short Time

This paper presents a fast adaptive time–frequency analysis method for dealing with the signals consisting of stationary components and transients, which are encountered very often in practice. It is developed based on the short-time Fourier transform but the window bandwidth varies along frequency adaptively. The method therefore behaves more like an adaptive continuous wavelet transform. We use B-splines as the window functions, which have near optimal time–frequency localization, and derive a fast algorithm for adaptive time–frequency representation. The method is applied to the analysis of vibration signals collected from rotating machines with incipient localized defects. The results show that it performs obviously better than the short-time Fourier transform, continuous wavelet transform, and several other most studied time–frequency analysis techniques for the given task.

scholarly journals A combined generalized Warblet transform and second order synchroextracting transform for analyzing nonstationary signals of rotating machinery

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Kai Wei ◽  
Xuwen Jing ◽  
Bingqiang Li ◽  
Chao Kang ◽  
Zhenhuan Dou ◽  
...  
Keyword(s):  
Vibration Signal ◽  
Rotating Machinery ◽  
Second Order ◽  
Variable Speed ◽  
Short Time Fourier Transform ◽  
Stationary Characteristic ◽  
Nonstationary Signals ◽  
Time Frequency ◽  
Effective Technology ◽  
Short Time

AbstractIn recent years, considerable attention has been paid in time–frequency analysis (TFA) methods, which is an effective technology in processing the vibration signal of rotating machinery. However, TFA techniques are not sufficient to handle signals having a strong non-stationary characteristic. To overcome this drawback, taking short-time Fourier transform as a link, a TFA methods that using the generalized Warblet transform (GWT) in combination with the second order synchroextracting transform (SSET) is proposed in this study. Firstly, based on the GWT and SSET theories, this paper proposes a method combining the two TFA methods to improve the TFA concentration, named GWT–SSET. Secondly, the method is verified numerically with single-component and multi-component signals, respectively. Quantized indicators, Rényi entropy and mean relative error (MRE) are used to analyze the concentration of TFA and accuracy of instantly frequency (IF) estimation, respectively. Finally, the proposed method is applied to analyze nonstationary signals in variable speed. The numerical and experimental results illustrate the effectiveness of the GWT–SSET method.

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