Linear Time-frequency Representations Research Articles

Weight extracting transform for instantaneous frequency estimation and signal reconstruction

This paper introduces a novel time–frequency analysis method called the Weight Extracting Transform (WET). The primary objective of WET is to enhance the energy concentration in linear time–frequency representations for time-varying signals. By aggregating the time–frequency blur produced by the short-time Fourier transform onto the actual instantaneous frequency, WET improves the readability and accuracy of the time–frequency representation. Additionally, the algorithm is extended to a more general linear time–frequency transform known as the chirplet transform, which effectively handles fast-varying signals. The WET method excels at distinguishing components with closely spaced instantaneous frequencies and can reconstruct the original signal from its time–frequency representation. Experimental results using simulated and real-world signals demonstrate that WET achieves superior energy concentration and noise robustness compared to existing methods.

Polarimetric Direction of Arrival Estimations Based on Adaptive Linear Time-Frequency Transforms

A spatially polarized time-frequency distribution (SPTFD) based on dual-polarized double-fed antenna arrays is adapted to deal with polarization-unstable signals. A linear time-frequency (TF) representation was used for an instantaneous frequency (IF) estimate, primarily due to its simplicity and immunity to cross-interference. Using a set of linear TF transformations using Gaussian windows and Fourier oscillation kernels, the IF estimated window widths of multiple unstable signals are obtained. This paper introduces a new method for estimating the direction of arrival (DOA) of polarized waves using adaptive linear time-frequency transforms. In this paper, a narrowband far-field point source on the receiving array is analyzed. The source signal is split into two orthogonally polarized components. The optimal window is determined by the first derivative of the IF; for this purpose, we take a simple algorithm for solving the derivative and optimize it. In developing TF-adaptive and fully automatic TF display technology, the first method is to use the time-adaptive window for minimizing the IF estimate mean square error (MSE) sum at each moment, while the second procedure is to adjust according to time and frequency and minimize estimate MSE sum at each position in the TF region. Due to its combination with signal polarization, the spatial time-frequency distribution (STFD) gains more freedom and thus perfects the phonon space estimation of noise and signal. On the SPTFD platform, polarized time-frequency multiple signal classification (PTF-MUSIC) is used for the estimation of signal direction of arrival, which outperforms conventional time-frequency MUSIC. Using the example of a synthesized signal, this method outperforms conventional techniques in DOA estimation.

Resonance based separation and energy based classification of lung sounds using tunable wavelet transform

Background and objectiveThe locations and occurrence pattern of adventitious sounds in the respiratory cycle have critical diagnostic information. In a lung sound sample, the crackles and wheezes may exist individually or they may coexist in a successive/overlapping manner superimposed onto the breath noise. The performance of the linear time-frequency representation based signal decomposition methods has been limited in the crackle/wheeze separation problem due to the common signal components that may arise in both time and frequency domain. However, the proposed resonance based decomposition can be used to isolate crackles and wheezes which behave oppositely in time domain even if they share common frequency bands. MethodsIn the proposed study, crackle and/or wheeze containing synthetic and recorded lung-sound signals were decomposed by using the resonance information which is produced by joint application of the Tunable Q-factor Wavelet Transform and Morphological Component Analysis. The crackle localization and signal reconstruction performance of the proposed approach was compared with the previously suggested Independent Component Analysis and Empirical Mode Decomposition methods in a quantitative and qualitative manner. Additionally, the decomposition ability of the proposed approach was also used to discriminate crackle and wheeze waveforms in an unsupervised way by employing signal energy. ResultsResults have shown that the proposed approach has significant superiority over its competitors in terms of the crackle localization and signal reconstruction ability. Moreover, the calculated energy values have revealed that the transient crackles and rhythmic wheezes can be successfully decomposed into low and high resonance channels by preserving the discriminative information. ConclusionsIt is concluded that previous works suffer from deforming the waveform of the crackles whose time domain parameters are vital in computerized diagnostic classification systems. Therefore, a method should provide automatic and simultaneous decomposition ability, with smaller root mean square error and higher accuracy as demonstrated by the proposed approach.

Linear and quadratic time frequency transforms on FPGA using folding technique

In this paper time frequency representations (TFRs) are implemented on FPGA. Linear TFRs such as Short Time Fourier Transform (STFT), Continuous Wavelet Transform (CWT), Stockwell Transform (S-Transform) and Quadratic TFRs like Wigner Ville Distribution (WVD), Pseudo Wigner Ville Distribution (PWVD), Choi William Distribution (CWD), and Rihaczek Distribution (RD) are designed in Verilog and performed over FPGA. In most of the FFT architectures many butterfly unit (BU) stages are remains idle during computation since current stage computation depends on previous stage outputs. As a result these idle BU leads to additional register allocation and delay propagation. An optimized VLSI architecture is proposed in this paper for efficient clock utilization to compute FFT in all TFRs. Folding technique is implemented in all TFRs to minimize the register allocation. The design is carried out in Verilog code and CORDIC algorithm is used tocomputecorebutterflystructureofFFTinallTFRs. Chirp signal is taken as input to evaluate real time performances of all TFRs. Real time factors utilized on FPGA hardware like Flip Flops, IOBs, LUTs utilization and power consumption are compared for allTFRs. Further proposed methodology is compared with previous existing methods for better time frequency applications.

Fully Adaptive Ridge Detection Based on STFT Phase Information

This letter deals with the problem of the estimation of the instantaneous frequencies of the modes of multicomponent signals from their linear time-frequency representations. In most approaches, such an estimation consists of extracting the ridges associated with each mode in the time-frequency plane. A major issue associated with these techniques is that ridge detection relies on some ad-hoc parameters which essentially bound the modulation of the studied modes and put some constraints on the type of filter used in the time-frequency representation. In this paper, we alternatively propose a novel fully adaptive approach for ridge detection whose relevance is shown throughout numerical simulations.

Adaptive Instantaneous Frequency Estimation of Multicomponent Signals Based on Linear Time–Frequency Transforms

The use of linear time-frequency (TF) representa-tions as instantaneous frequency (IF) estimators arises in various fundamental disciplines, mainly thanks to their simplicity and immunity against interfering cross-terms. In this paper, we derive the optimal window width for IF estimation of noisy multicomponent signals based on a family of linear TF transforms that use Gaussian windowing functions and the Fourier oscillatory kernel. Closed-form formulas concerning the estimation bias and the variance are presented, which, thanks to their generality, describe the statistical performance of IF estimators based on transforms with fixed, time-adaptive, frequency-adaptive, or time-frequency adaptive windows. The optimal window is dependent on the unknown first derivative of the IF; therefore, we employ a low-complexity procedure to infer the derivative and optimize the width accordingly. Two adaptive and fully automated TF representations (TFRs) are developed; the first employs a time-adaptive window that minimizes the sum of the mean-squared errors (MSEs) of the IF estimates at each time instant, while in the second TFR, the window is adaptive over time and frequency, minimizing the estimation MSE at each location in the TF domain. Examples using synthetic and real-world signals demonstrate that the proposed algorithms may outperform many popular state-of-the-art techniques, including those that are signal-adaptive, in terms of IF estimation.

Assessment of Time Frequency Color Index for Electrical Machines Diagnosis and Fault Severity

Improving availability and reliability of Induction Machine (IM) implies the minimization and the prediction of the maintenance operations. In this paper, we focus on detection and location of the rotor electrical faults in IM. This kind of fault generates non-stationary signatures in the stator current of the machine. Advanced signal processing techniques are required to deal with that type of signals. In this context, several recent studies suggest the use of Time-Frequency Representations (TFR) for the diagnosis of IMs' faults. This work presents a comparative study of some linear TFR. This last relies on good experimental results conducted on a test bench using a wound rotor induction machine operating in no load condition. The purpose is to showcase the TFR performances in faults detection. Static indicator is used to check the fault severity.

A new time-frequency method to reveal quantum dynamics of atomic hydrogen in intense laser pulses: Synchrosqueezing transform

This study introduces a new adaptive time-frequency (TF) analysis technique, the synchrosqueezing transform (SST), to explore the dynamics of a laser-driven hydrogen atom at an ab initio level, upon which we have demonstrated its versatility as a new viable venue for further exploring quantum dynamics. For a signal composed of oscillatory components which can be characterized by instantaneous frequency, the SST enables rendering the decomposed signal based on the phase information inherited in the linear TF representation with mathematical support. Compared with the classical type of TF methods, the SST clearly depicts several intrinsic quantum dynamical processes such as selection rules, AC Stark effects, and high harmonic generation.

Adapted and Adaptive Linear Time-Frequency Representations: A Synthesis Point of View

A large variety of techniques exist to display the time and frequency content of a given signal. In this article, we give an overview of linear time-frequency representations, focusing mainly on two fundamental aspects. The first is the introduction of flexibility, more precisely, the construction of time-frequency waveform systems that can be adapted to specific signals or specific signal processing problems. To do this, we base the constructions on frame theory, which allows many options while still ensuring perfect reconstruction. The second aspect is the choice of the synthesis framework rather than the usual analysis framework. Instead of considering the correlation, i.e. the inner product, of the signal with the chosen waveforms, we find appropriate coefficients in a linear combination of those waveforms to synthesize the given signal. We show how this point of view allows the easy introduction of prior information into the representation. We give an overview of methods for transform domain modeling, in particular those based on sparsity and structured sparsity. Finally, we present an illustrative application for these concepts: a denoising scheme.

Automated segmentation of linear time-frequency representations of marine-mammal sounds

Many marine mammals produce highly nonlinear frequency modulations. Determining the time-frequency support of these sounds offers various applications, which include recognition, localization, and density estimation. This study introduces a low parameterized automated spectrogram segmentation method that is based on a theoretical probabilistic framework. In the first step, the background noise in the spectrogram is fitted with a Chi-squared distribution and thresholded using a Neyman-Pearson approach. In the second step, the number of false detections in time-frequency regions is modeled as a binomial distribution, and then through a Neyman-Pearson strategy, the time-frequency bins are gathered into regions of interest. The proposed method is validated on real data of large sequences of whistles from common dolphins, collected in the Bay of Biscay (France). The proposed method is also compared with two alternative approaches: the first is smoothing and thresholding of the spectrogram; the second is thresholding of the spectrogram followed by the use of morphological operators to gather the time-frequency bins and to remove false positives. This method is shown to increase the probability of detection for the same probability of false alarms.

Compressive Sensing Based Separation of Nonstationary and Stationary Signals Overlapping in Time-Frequency

A compressive sensing (CS) approach for nonstationary signal separation is proposed. This approach is motivated by challenges in radar signal processing, including separations of micro-Doppler and main body signatures. We consider the case where the signal of interest assumes sparse representation over a given basis. Other signals present in the data overlap with the desired signal in the time and frequency domains, disallowing conventional windowing or filtering operations to be used for desired signal recovery. The proposed approach uses linear time-frequency representations to reveal the data local behavior. Using the L-statistics, only the time-frequency (TF) points that belong to the desired signal are retained, whereas the common points and others pertaining only to the undesired signals are deemed inappropriate and cast as missing samples. These samples amount to reduced frequency observations in the TF domain. The linear relationship between the measurement and sparse domains permits the application of CS techniques to recover the desired signal without significant distortion. We focus on sinusoidal desired signals with sparse frequency-domain representation but show that the analysis can be straightforwardly generalized to nonsinusoidal signals with known structures. Several examples are provided to demonstrate the effectiveness of the proposed approach.

Efficient Localization of Hot Spots in Proteins Using a Novel S-Transform Based Filtering Approach

Protein-protein interactions govern almost all biological processes and the underlying functions of proteins. The interaction sites of protein depend on the 3D structure which in turn depends on the amino acid sequence. Hence, prediction of protein function from its primary sequence is an important and challenging task in bioinformatics. Identification of the amino acids (hot spots) that leads to the characteristic frequency signifying a particular biological function is really a tedious job in proteomic signal processing. In this paper, we have proposed a new promising technique for identification of hot spots in proteins using an efficient time-frequency filtering approach known as the S-transform filtering. The S-transform is a powerful linear time-frequency representation and is especially useful for the filtering in the time-frequency domain. The potential of the new technique is analyzed in identifying hot spots in proteins and the result obtained is compared with the existing methods. The results demonstrate that the proposed method is superior to its counterparts and is consistent with results based on biological methods for identification of the hot spots. The proposed method also reveals some new hot spots which need further investigation and validation by the biological community.

Identification of Protein-Coding Regions in DNA Sequences Using A Time-Frequency Filtering Approach

Accurate identification of protein-coding regions (exons) in DNA sequences has been a challenging task in bioinformatics. Particularly the coding regions have a 3-base periodicity, which forms the basis of all exon identification methods. Many signal processing tools and techniques have been applied successfully for the identification task but still improvement in this direction is needed. In this paper, we have introduced a new promising model-independent time-frequency filtering technique based on S-transform for accurate identification of the coding regions. The S-transform is a powerful linear time-frequency representation useful for filtering in time-frequency domain. The potential of the proposed technique has been assessed through simulation study and the results obtained have been compared with the existing methods using standard datasets. The comparative study demonstrates that the proposed method outperforms its counterparts in identifying the coding regions.

Superposition Frames for Adaptive Time-Frequency Analysis and Fast Reconstruction

In this article we introduce a broad family of adaptive, linear time-frequency representations termed superposition frames, and show that they admit desirable fast overlap-add reconstruction properties akin to standard short-time Fourier techniques. This approach stands in contrast to many adaptive time-frequency representations in the extant literature, which, while more flexible than standard fixed-resolution approaches, typically fail to provide efficient reconstruction and often lack the regular structure necessary for precise frame-theoretic analysis. Our main technical contributions come through the development of properties which ensure that this construction provides for a numerically stable, invertible signal representation. Our primary algorithmic contributions come via the introduction and discussion of specific signal adaptation criteria in deterministic and stochastic settings, based respectively on time-frequency concentration and nonstationarity detection. We conclude with a short speech enhancement example that serves to highlight potential applications of our approach.

Adaptive noise and interference removal from speech based on a modified short time Fourier transform.

A simple linear adaptive method for removing noise and interference from speech is presented. The method is based on a linear time-frequency representation in which the short time Fourier transform (STFT) is concentrated (reassigned) in frequency. The concentration process results in a complex-valued surface in which speech components and narrowband AM/FM interference components are essentially time-varying spectral impulses. Unwanted components may be removed from the surface, and the clean signal with these components removed may be reconstructed as a linear time marginal, computed by integrating the surface with respect to frequency. This process is linear and results in a nearly distortion-free reconstructed signal. Moreover, unlike processes like methods such as spectral subtraction, the process requires no Fourier inversion. This process is computationally efficient since the STFT is implemented as a bank of recursive two tap filters.

Hilbert-Huang versus Morlet wavelet transformation on mismatch negativity of children in uninterrupted sound paradigm

BackgroundCompared to the waveform or spectrum analysis of event-related potentials (ERPs), time-frequency representation (TFR) has the advantage of revealing the ERPs time and frequency domain information simultaneously. As the human brain could be modeled as a complicated nonlinear system, it is interesting from the view of psychological knowledge to study the performance of the nonlinear and linear time-frequency representation methods for ERP research. In this study Hilbert-Huang transformation (HHT) and Morlet wavelet transformation (MWT) were performed on mismatch negativity (MMN) of children. Participants were 102 children aged 8–16 years. MMN was elicited in a passive oddball paradigm with duration deviants. The stimuli consisted of an uninterrupted sound including two alternating 100 ms tones (600 and 800 Hz) with infrequent 50 ms or 30 ms 600 Hz deviant tones. In theory larger deviant should elicit larger MMN. This theoretical expectation is used as a criterion to test two TFR methods in this study. For statistical analysis MMN support to absence ratio (SAR) could be utilized to qualify TFR of MMN.ResultsCompared to MWT, the TFR of MMN with HHT was much sharper, sparser, and clearer. Statistically, SAR showed significant difference between the MMNs elicited by two deviants with HHT but not with MWT, and the larger deviant elicited MMN with larger SAR.ConclusionSupport to absence ratio of Hilbert-Huang Transformation on mismatch negativity meets the theoretical expectations, i.e., the more deviant stimulus elicits larger MMN. However, Morlet wavelet transformation does not reveal that. Thus, HHT seems more appropriate in analyzing event-related potentials in the time-frequency domain. HHT appears to evaluate ERPs more accurately and provide theoretically valid information of the brain responses.

An Overcomplete Signal Basis Approach to Nonlinear Time-Tone Analysis with Application to Audio and Speech Processing

Although a beating tone and the two pure tones which give rise to it are linearly dependent, the ear considers them to be independent as tone sensations. A linear time-frequency representation of acoustic data is unable to model these phenomena. A time-tone sensation approach is proposed for inclusion within audio analysis systems. The proposed approach extends linear time-frequency analysis of acoustic data, by accommodating the nonlinear phenomenon of beats. The method replaces the one-dimensional tonotopic axis of linear time-frequency analysis with a two-dimensional tonotopic plane, in which one direction corresponds to tone, and the other to its frequency of modulation. Some applications to audio prostheses are discussed. The proposed method relies on an intuitive criterion of optimal representation which can be applied to any overcomplete signal basis, allowing for many signal processing applications.

Use of instantaneous estimators for the evaluation of structural damping

This study focuses on the definition of time–frequency instantaneous estimators to be employed in the identification of structural damping from signals measured in ambient vibration conditions. The estimators discussed here are obtained from instantaneous curve fitting applied directly to time–frequency representations of dynamic response signals. One of the strong points of this technique is its flexibility: from each signal, a time function of modal damping and amplitude is extracted, providing punctual information on the stability and consistency of damping estimate. The aim of this paper is to study the implications related to the use of this method with linear time–frequency representations. Linear representations, within the inherent limits of their linear nature, still retain attractive computational advantages and lend themselves to a clear theoretical interpretation. In the last part of the paper, a series of numerical applications to simple systems is presented to support theoretical argumentations. Finally, an experimental application to the identification of the damping in a real concrete building is shown.

Use of instantaneous estimators for the evaluation of structural damping

This study focuses on the definition of time–frequency instantaneous estimators to be employed in the identification of structural damping from signals measured in ambient vibration conditions. The estimators discussed here are obtained from instantaneous curve fitting applied directly to time–frequency representations of dynamic response signals. One of the strong points of this technique is its flexibility: from each signal, a time function of modal damping and amplitude is extracted, providing punctual information on the stability and consistency of damping estimate. The aim of this paper is to study the implications related to the use of this method with linear time–frequency representations. Linear representations, within the inherent limits of their linear nature, still retain attractive computational advantages and lend themselves to a clear theoretical interpretation. In the last part of the paper, a series of numerical applications to simple systems is presented to support theoretical argumentations. Finally, an experimental application to the identification of the damping in a real concrete building is shown.

Short-time fourier transform: two fundamental properties and an optimal implementation

Shift and rotation invariance properties of linear time-frequency representations are investigated. It is shown that among all linear time-frequency representations, only the short-time Fourier transform (STFT) family with the Hermite-Gaussian kernels satisfies both the shift invariance and rotation invariance properties that are satisfied by the Wigner distribution (WD). By extending the time-bandwidth product (TBP) concept to fractional Fourier domains, a generalized time-bandwidth product (GTBP) is defined. For mono-component signals, it is shown that GTBP provides a rotation independent measure of compactness. Similar to the TBP optimal STFT, the GTBP optimal STFT that causes the least amount of increase in the GTBP of the signal is obtained. Finally, a linear canonical decomposition of the obtained GTBP optimal STFT analysis is presented to identify its relation to the rotationally invariant STFT.