Composite wavelet transform and frames

P01-Comparison of short-time Fourier transform and continuous wavelet transform for frequency analysis of sleep EEG

Aiming reliable detection and localization of cerebral blood flow and emboli, embolic signals were added to simulated middle cerebral artery Doppler signals and analysed. Short-time Fourier transform (STFT) and continuous wavelet transform (CWT) were used in the evaluation. The following parameters were used in this study: the powers of the embolic signals added were 5, 6, 6.5, 7, 7.5, 8 and 9 dB; the mother wavelets for CWT analysis were Morlet, Mexican hat, Meyer, Gaussian (order 4) and Daubechies (orders 4 and 8); and the thresholds for detection (equated in terms of false positive, false negative and sensitivity) were 2 and 3.5 dB for the CWT and STFT, respectively. The results indicate that although the STFT allows accurately detecting emboli, better time localization can be achieved with the CWT. Among the CWT, the current best overall results were obtained with Mexican Hat mother wavelet, with optimal results for sensitivity (100% detection rate) for nearly all emboli power values studied.

The short time Fourier transform (STFT) cannot resolve rapid velocity changes in most photonic Doppler velocimetry (PDV) data. A practical analysis method based on the continuous wavelet transform (CWT) was presented to overcome this difficulty. The adaptability of the wavelet family predicates that the continuous wavelet transform uses an adaptive time window to estimate the instantaneous frequency of signals. The local frequencies of signal are accurately determined by finding the ridge in the spectrogram of the CWT and then are converted to target velocity according to the Doppler effects. A performance comparison between the CWT and STFT is demonstrated by a plate-impact experiment data. The results illustrate that the new method is automatic and adequate for analysis of PDV data.

Frequency domain analyses in electromyographic (EMG) signals are frequently applied to assess muscle fatigue and similar variables. Moreover, Fourier-based approaches are typically used for investigating these procedures. Nonetheless, Fourier analysis assumes the signal as stationary which is unlikely during dynamic contractions. As an alternative method, wavelet-based treatments do not assume this pattern and may be considered as more appropriate for joint time-frequency domain analysis. Based on the previous statements, the purpose of the present study was to compare the application of Short-Time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT) to assess muscle fatigue in dynamic exercise of a 1-km of cycling (time-trial condition). The results of this study indicated that CWT and STFT analyses have provided similar fatigue estimates (slope) (p> 0.05). However, CWT application represents lesser dispersion (pp> 0.05) according to different methods, it is important to note that these responses seem to show greater values for CWT compared to STFT for 2 superficial muscles. Thereby, we are capable of considering CWT as a reliable and useful method to take into consideration when non-stationary or oscillating exercise models are evaluated.

The continuous wavelet transform (CWT) and the short-time Fourier transform (STFT) are used to analyze the time course of cellular motion in the guinea-pig inner ear. The velocity responses of individual auditory cells (outer hair cells and Hensen's cells) to amplitude-modulated (AM) acoustical signals display characteristics typical of nonlinear systems, such as harmonic generation. Nonlinear effects are particularly pronounced at the highest stimulus levels, where half-harmonic, and sometimes quarter-harmonic, components are also seen. Both the CWT and the STFT are found to be useful in analyzing these velocity responses. The authors carry out CWT analyses using a Morlet wavelet and an AM wavelet, and find the results are quite similar. >

Epilepsy is one of the most common neurological disorders. Epileptic seizures are the manifestation of abnormal hypersynchronous discharges of cortical neurons that impair brain function. Most of the people affected can be treated successfully with drug therapy or neurosurgical procedures. But there is still a large group of epilepsy patients that continues to have frequent seizures. For these patients automated detection of epileptic seizures can be of great clinical importance. Seizure detection can influence daily care or can be used to evaluate treatment effect. Furthermore automated detection can be used to trigger an alarm system during seizures that might be harmful to the patient. This thesis focusses on accelerometry (ACM) based seizure detection. A detailed overview is provided, on the perspectives for long-term epilepsy monitoring and automated seizure detection. The value of accelerometry for seizure detection is shown by means of a clinical evaluation and the first steps are made towards automatic detection of epileptic seizures based on ACM. With accelerometers movements are recorded. A large group of epileptic seizures manifest in specific movement patterns, so called motor seizures. Chapter 2 of this thesis presents an overview of the published literature on available methods for epileptic seizure detection in a long-term monitoring context. Based on this overview recommendations are formulated that should be used in seizure detection research and development. It is shown that for seizure detection in home environments, other sensor modalities besides EEG become more important. The use of alternative sensor modalities (such as ACM) is relatively new and so is the algorithm development for seizure detection based on these measures. It was also found that for both the adaptation of existing techniques and the development of new algorithms, clinical information should be taken more into account. The value of ACM for seizure detection is shown by means of a clinical evaluation in chapter 3. Here 3-D ACM- and EEG/video-recordings of 18 patients with severe epilepsy are visually analyzed. A striking outcome presented in this chapter is the large number of visually detected seizures versus the number of seizures that was expected on forehand and the number of seizures that was observed by the nurses. These results underscore the need for an automatic seizure detection device even more, since in the current situation many seizures are missed and therefore it is possible that patients do not get the right (medical) treatment. It was also observed that 95% of the ACM-patterns during motor seizures are sequences of three elementary patterns: myoclonic, tonic and clonic patterns. These characteristic patterns are a starting point for the development of methods for automated seizure detection based on ACM. It was decided to use a modular approach for the detection methodology and develop algorithms separately for motor activity in general, myoclonic seizures and tonic seizures. Furthermore, clinical information is incorporated in the detection methodology. Therefore in this thesis features were used that are either based on the shape of the patterns of interest as described in clinical practice (chapter 4 and 7), or the features were based on a physiological model with parameters that are related to seizure duration and intensity (chapter 5 and 6). In chapter 4 an algorithm is developed to distinguish periods with and without movement from ACM-data. Hence, when there is no movement there is no motor seizure. The amount of data that needs further analysis for seizure detection is thus reduced. From 15 ACM-signals (measured on five positions on the body), two features are computed, the variance and the jerk. In the resulting 2-D feature space a linear threshold function is used for classification. For training and testing the algorithm ACM data along with video data are used from nocturnal recordings in mentally retarded patients with severe epilepsy. Using this algorithm the amount of data that needs further analysis is reduced considerably. The results also indicate that the algorithm is robust for fluctuations across patients and thus there is no need for training the algorithm for each new patient. For the remaining data it needs to be established whether the detected movement is seizure related or not. To this purpose a model is developed for the accelerometer pattern measured on the arm during a myoclonic seizure (chapter 5). The model consists of a mechanical and an electrophysiological part. This model is used as a matched wavelet filter to detect myoclonic seizures. In chapter 6 the model based wavelet is compared to three other time frequency measures: the short time Fourier transform, the Wigner distribution and the continuous wavelet transform using a Daubechies wavelet. All four time-frequency methods are evaluated in a linear classification setup. Data from mentally retarded patients with severe epilepsy are used for training and evaluation. The results show that both wavelets are useful for detection of myoclonic seizures. On top of that, our model based wavelet has the advantage that it consists of parameters that are related to seizure duration and intensity that are physiological meaningful. Besides myoclonic seizures, the model is also useful for the detection of clonic seizures; physiologically these are repetitive myoclonic seizures. Finally for the detection of tonic seizures, in chapter 7 a set of features is studied that incorporate the mean characteristics of ACM-patterns associated with tonic seizures. Linear discriminant analysis is used for classification in the multi-dimensional feature space. For training and testing the algorithm, again data are used from recordings in mentally retarded patients with severe epilepsy. The results show that our approach is useful for the automated detection of tonic seizures based on 3-D ACM and that it is a promising contribution in a complete multi-sensor seizure detection setup.

Frequency domain analyses of changes in electromyographic (EMG) signals over time are frequently used to assess muscle fatigue. Fourier based approaches are typically used in these analyses, yet Fourier analysis assumes signal stationarity, which is unlikely during dynamic contractions. Wavelet based methods of signal analysis do not assume stationarity and may be more appropriate for joint time-frequency domain analysis. The purpose of this study was to compare Short-Time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT) in assessing muscle fatigue in supramaximal constant load dynamic exercise (110% VO(2peak)). The results of this study indicate that CWT and STFT analyses give similar fatigue estimates (slope of median frequency) in supramaximal constant load dynamic exercise (P>0.05). However, the results of the variance was significantly lower for at least one of the muscles studied in CWT compared to STFT (P < 0.05) indicating more variability in the EMG signal analysis using STFT. Thus, the stationarity assumption may not be the sole factor responsible for affecting the Fourier based estimates.

Time–frequency analysis of the baroreflex control of renal sympathetic nerve activity in the rat

In field harvesting conditions, the non-stationary random vibration characteristics of the harvester are rarely considered, and the results of vibration frequency calculated by different time–frequency transformation methods are different. In this paper, the harvester’s vibration characteristics under the time-varying mass were studied, and the correlation between vibration frequency and modal frequency was analyzed. Firstly, under the conditions of time-varying mass (field harvesting conditions) and non-time-varying mass (empty running condition), the non-stationarity characteristics of vibration signals at 16 measurement points of a combined corn harvester frame were studied. Then, fast Fourier transform (FFT), short-time Fourier transform (STFT), and continuous wavelet transform (CWT) were used to calculate the vibration frequency distribution characteristics of the corn harvester. Finally, based on the EFDD (enhanced frequency domain decomposition) algorithm, the correlation between the primary vibration frequency and the operating mode frequency is studied. The results show that the mean, variance, and maximum difference of the vibration amplitude under harvesting conditions (mass time-varying system) are 0.10, 26.5, and 1.0, respectively, at different harvesting periods (0~10 s, 10~20 s, 20~30 s). The harvesting conditions’ vibration signals conform to the characteristics of non-stationary randomness. The FFT algorithm is used to obtain more dense vibration frequencies, while the frequencies based on STFT and CWT algorithms are sparse. The correlation between the FFT method and the EFDD algorithm is 0.98, and the correlation between the STFT, CWT, and the EFDD algorithm is 0.99 and 0.98. Therefore, the primary frequency of the STFT methods is closer to the modal frequency. Our research laid the foundation for further study and application of mass time-varying combined harvester system non-stationary random vibration modal frequency identification and vibration control.

Underwater acoustic target (UAT) classification is a critical task in submarine warfare because acoustic waves are the reliable information source that allows sonar operators and commanders to understand the surrounding situation in the operational area. To solve the problem of UAT classification, this paper proposes a convolutional neural network combined with continuous wavelet transform for improving the accuracy of UAT classification. The classification focuses on types of noise emitted from the propellers of different ships. Signal processing methods such as Short Time Fourier Transform, Continuous Wavelets Transform, and CNN are executed to extract signal features that provide information for classifier. Simulation results are achieved with an accuracy of 99.64\% when using the Continuous Wavelets Transform method combined with the convolutional neural network, which is higher than other traditional methods.

BackgroundTime-Frequency analysis of electroencephalogram (EEG) during different mental tasks received significant attention. As EEG is non-stationary, time-frequency analysis is essential to analyze brain states during different mental tasks. Further, the time-frequency information of EEG signal can be used as a feature for classification in brain-computer interface (BCI) applications.MethodsTo accurately model the EEG, band-limited multiple Fourier linear combiner (BMFLC), a linear combination of truncated multiple Fourier series models is employed. A state-space model for BMFLC in combination with Kalman filter/smoother is developed to obtain accurate adaptive estimation. By virtue of construction, BMFLC with Kalman filter/smoother provides accurate time-frequency decomposition of the bandlimited signal.ResultsThe proposed method is computationally fast and is suitable for real-time BCI applications. To evaluate the proposed algorithm, a comparison with short-time Fourier transform (STFT) and continuous wavelet transform (CWT) for both synthesized and real EEG data is performed in this paper. The proposed method is applied to BCI Competition data IV for ERD detection in comparison with existing methods.ConclusionsResults show that the proposed algorithm can provide optimal time-frequency resolution as compared to STFT and CWT. For ERD detection, BMFLC-KF outperforms STFT and BMFLC-KS in real-time applicability with low computational requirement.

Time-Frequency signal analysis represents the function in both time and frequency domains by the calculation of the spectrum at regular intervals of time. Moreover, Time-Frequency analysis is based on Fourier Transform. There are several Time-Frequency distribution functions such as Short-Time Fourier Transform (STFT), Continuous Wavelet Transform (CWT), and Wigner Ville Transform (WVT). This article focuses on chafed faults detection by using STFT, CWT, and WVT. Finally, a comparison of these approaches' performances is made.

Among a variety of spectrogram methods Short-Time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT) were selected to analyse transients in non-stationary tremor signals. Depending on the properties of the tremor signal a more suitable representation of the signal is gained by CWT. Three selected broadband tremor signals from the volcanos Mt. Stromboli, Mt. Semeru and Mt. Pinatubo were analyzed using both methods. The CWT can also be used to extend the definition of coherency into a time-varying coherency spectrogram. An example is given using array data from the volcano Mt. Stromboli.

Time-frequency (TF) characterization of electromyographic (EMG) bursts is essential for accurately assessing muscle function, particularly when the signals exhibit a high degree of nonstationarity. In this exploratory study, we investigated the temporal dynamics of the spectral components associated with short-latency EMG bursts using several TF analysis techniques. Specifically, we compared the performance and interpretability of spectrograms obtained via the short-time Fourier transform (STFT), the continuous wavelet transform (CWT), and noise-assisted multivariate empirical mode decomposition (NA-MEMD), applied to EMG signals recorded from the biceps femoris muscle of freely moving rats in an animal model of Parkinson's disease, acquired using chronically implanted bipolar electrodes during treadmill locomotion. For each method, we evaluated its effectiveness in capturing transient variations in frequency content, the stability of extracted features across bursts, and the extent to which these features reflect physiologically meaningful aspects of muscle activation. The results show that TF approaches reveal complementary information about burst structure; NA-MEMD provides greater adaptability to nonlinear and nonstationary components, whereas STFT- and CWT-based representations offer more controlled and comparable analyses. Overall, these findings highlight the value of TF analysis as a methodological tool for evaluating muscle function and provide a solid foundation for selecting analytical strategies in studies where EMG bursts exhibit complex and highly variable spectral profiles.

Summary Conventional seismic sections cannot display most of the important events in reservoir studies. The study of frequency content of seismic sections can provide better understanding to geoscientists, as well as interpreters in the field of petroleum engineering studies. An isofrequency process is a powerful tool in terms of reservoir imaging. One of the methods that provides isofrequency slice is Spectral Decomposition (SD). SD is a comprehensive method that eliminates most of limitations encountered in seismic data to reveal geological information. SD provides continuous analysis of amplitude, frequency, phase, and energy spectrum. Therefore, SD is applied to obtain an amplitude spectrum of frequency content of seismic trace which is attributed to the temporal center of the sample trace. So higher frequency resolution is obtained at lower frequencies and higher time resolution at higher frequencies. In this paper, Short Time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT) as SD methods were used in order to detect sand channel at one of the Iranian Southwest oil fields for which it has the potential to be considered as a reservoir.