Time/frequency events of surface mechanomyographic signals resolved by nonlinearly scaled wavelets

The purpose of this investigation is to introduce a wavelet analysis designed for analyzing short events reflecting bursts of muscle activity in non-stationary mechanomyographic (MMG) signals. A filter bank of eleven nonlinearly scaled wavelets that maintain the optimal combination of time and frequency resolution across the frequency range of MMG signals (5–100 Hz) was used for the analysis. A comparison with the short-time Fourier transform, Wigner-Ville transform and continuous wavelet transform using a test signal with known time–frequency characteristics showed that the MMG wavelet analysis resolved the intensity, timing, and frequencies of events in a more distinct way without overemphasizing high or low frequencies or generating interference terms. The analysis was used to process MMG signals from the vastus lateralis, rectus femoris, and vastus medialis muscles obtained during maximal concentric and eccentric isokinetic movements. Muscular events were observed that were precisely located in time and frequency in a muscle-specific way, thereby showing periods of synergistic contractions of the quadriceps muscles. The MMG wavelet spectra showed different spectral bands for concentric and eccentric isokinetic movements. In addition, the high and low frequency bands seemed to be activated independently during the isokinetic movement. What generates these bands is not yet known, however, the MMG wavelet analysis was able to resolve them, and is therefore applicable to non-stationary MMG signals.     

Wavelet and Fourier analysis of ventricular and main arteries pulsations in anesthetized dogs

The purpose of this study was to characterize time-frequency behavior using the Continuous Wavelet Transform (CWT) and Fast Fourier Transform (FFT) to analyze ventricular and arterial pressure signals from anesthetized mongrel dogs. Both ventricular and arterial pressure pulsations were recorded using catheter-tip manometers and the CWT was applied to these signals to obtain module coefficients, associated contours, and the 3-D representation of these modules. FFT was applied to obtain the Fourier spectrum. The mathematical analysis of the cardiovascular pressure pulsations permitted the identification of the evolution of the frequency components for the aortic and pulmonary valve functions as well as the intra-ventricular and respiratory influences on the cardiovascular dynamics. The CWT is a very sensitive and reliable procedure for determining the three-dimensional (time-frequency-amplitude) of the oscillatory phenomena during each cardiac cycle, providing more, although complementary, information than the spectral analysis obtained with the FFT. Thanks to the FFT, exact values in Hz could be found for the different events produced in each cycle, and thus the information provided by CWT could be related to the information provided by FFT. The combination of both mathematical methodologies permitted identification of each component of the analyzed signals. The 3D representation allowed an easy comparison of the relative importance of the complex magnitudes in frequency for the different components of the pulsatile waves.     

Application of competitive Hopfield neural network to brain-computer interface systems

We propose an unsupervised recognition system for single-trial classification of motor imagery (MI) electroencephalogram (EEG) data in this study. Competitive Hopfield neural network (CHNN) clustering is used for the discrimination of left and right MI EEG data posterior to selecting active segment and extracting fractal features in multi-scale. First, we use continuous wavelet transform (CWT) and Student's two-sample t-statistics to select the active segment in the time-frequency domain. The multiresolution fractal features are then extracted from wavelet data by means of modified fractal dimension. At last, CHNN clustering is adopted to recognize extracted features. Due to the characteristic of non-supervision, it is proper for CHNN to classify non-stationary EEG signals. The results indicate that CHNN achieves 81.9% in average classification accuracy in comparison with self-organizing map (SOM) and several popular supervised classifiers on six subjects from two data sets.     

Dynamical correlation of non-stationary signals in time domain—A comparative study

In a thorough study, the multitaper (MTM) and the extended continuous wavelet-transform (CWT) coherence-analysis methods were compared in terms of there application in determining the dynamics from the electroencephalogram (EEG) and electromyogram (EMG) signals of patients with Parkinsonian tremor. The main aim of the study in a biological point of view is to analyze whether the basic tremor frequency and its “first harmonic” frequency of Parkinsonian tremor are really harmonically related or are in fact distinct processes.The extension of the CWT is achieved by using a Morlet wavelet as the analysis window with an adjustable relative bandwidth which gives the flexibility in setting a desired frequency resolution. In order to obtain a perspective view of the two methods, they were applied to two different model signals to determine their actual threshold in detecting short-lived changes in the analysis of non-stationary signals and to determine their noise thresholds by adding external noise to the signals to test the reduction in coherence to be not merely due to the random fluctuations in stochastic signals. Beyond applying an autoregressive 2nd-order and a coupled van der Pol model system, however, also true EEG and EMG data from five Parkinson patients were used. The results were compared in terms of the time and frequency resolutions of these two methods, and it was determined that the multitaper method was able to detect reduction in power and coherence as short as 1 s. The extended CWT analysis only revealed gaps that were longer than 3 s.The time gaps in the coherence indicate the loss of connection between the cortex and muscle during the respective time intervals. This more accurate analysis of the MTM was also seen in the dynamical EEG–EMG coherence at the tremor frequency and its “first harmonic” of Parkinsonian patients.In terms of our “biological” aim, this shows distinct prevalence of the corticomuscular coupling at those frequencies over time. Applying this method to biological data reveals important aspects about their dynamics, e.g., the distinct dynamics between basic frequency and “first harmonic” frequency over time in Parkinsonian tremor.     

Time and frequency domain responses of the mechanomyogram and electromyogram during isometric ramp contractions: a comparison of the short-time Fourier and continuous wavelet transforms.

The purposes of this study were to examine the mechanomyographic (MMG) and electromyographic (EMG) time and frequency domain responses of the vastus lateralis (VL) and rectus femoris (RF) muscles during isometric ramp contractions and compare the time-frequency of the MMG and EMG signals generated by the short-time Fourier transform (STFT) and continuous wavelet transform (CWT). Nineteen healthy subjects (mean+/-SD age=24+/-4 years) performed two isometric maximal voluntary contractions (MVCs) before and after completing 2-3, 6-s isometric ramp contractions from 5% to 100% MVC with the right leg extensors. MMG and surface EMG signals were recorded from the VL and RF muscles. Time domains were represented as root mean squared amplitude values, and time-frequency representations were generated using the STFT and CWT. Polynomial regression analyses indicated cubic increases in MMG amplitude, MMG frequency, and EMG frequency, whereas EMG amplitude increased quadratically. From 5% to 24-28% MVC, MMG amplitude remained stable while MMG frequency increased. From 24-28% to 76-78% MVC, MMG amplitude increased rapidly while MMG frequency plateaued. From 76-78% to 100% MVC, MMG amplitude plateaued (VL) or decreased (RF) while MMG frequency increased. EMG amplitude increased while EMG frequency changed only marginally across the force spectrum with no clear deflection points. Overall, these findings suggested that MMG may offer more unique information regarding the interactions between motor unit recruitment and firing rate that control muscle force production during ramp contractions than traditional surface EMG. In addition, although the STFT frequency patterns were more pronounced than the CWT, both algorithms produced similar time-frequency representations for tracking changes in MMG or EMG frequency.     

Bayesian denoising framework of phonocardiogram based on a new dynamical model

In this paper, we introduce a model-based Bayesian denoising framework for phonocardiogram (PCG) signals. The denoising framework is founded on a new dynamical model for PCG, which is capable of generating realistic synthetic PCG signals. The introduced dynamical model is based on PCG morphology and is inspired by electrocardiogram (ECG) dynamical model proposed by McSharry et al. and can represent various morphologies of normal PCG signals. The extended Kalman smoother (EKS) is the Bayesian filter that is used in this study. In order to facilitate the adaptation of the denoising framework to each input PCG signal, the parameters are selected automatically from the input signal itself. This approach is evaluated on several PCGs recorded on healthy subjects, while artificial white Gaussian noise is added to each signal, and the SNR and morphology of the outputs of the proposed denoising approach are compared with the outputs of the wavelet denoising (WD) method. The results of the EKS demonstrate better performance than WD over a wide range of PCG SNRs. The new PCG dynamical model can also be employed to develop other model-based processing frameworks such as heart sound segmentation and compression.     

Intensity analysis in time-frequency space of surface myoelectric signals by wavelets of specified resolution

Surface myoelectric signals often appear to carry more information than what is resolved in root mean square analysis of the progress curves or in its power spectrum. Time-frequency analysis of myoelectric signals has not yet led to satisfactory results in respect of separating simultaneous events in time and frequency. In this study a time-frequency analysis of the intensities in time series was developed. This intensity analysis uses a filter bank of non-linearly scaled wavelets with specified time-resolution to extract time-frequency aspects of the signal. Special procedures were developed to calculate intensity in such a way as to approximate the power of the signal in time. Applied to an EMG signal the intensity analysis was called a functional EMG analysis. The method resolves events within the EMG signal. The time when the events occur and their intensity and frequency distribution are well resolved in the intensity patterns extracted from the EMG signal. Averaging intensity patterns from multiple experiments resolve repeatable functional aspects of muscle activation. Various properties of the functional EMG analysis were shown and discussed using model EMG data and real EMG data.     

Discrete wavelet transform analysis of surface electromyography for the fatigue assessment of neck and shoulder muscles

Assessment of neuromuscular fatigue is essential for early detection and prevention of risks associated with work-related musculoskeletal disorders. In recent years, discrete wavelet transform (DWT) of surface electromyography (SEMG) has been used to evaluate muscle fatigue, especially during dynamic contractions when the SEMG signal is non-stationary. However, its application to the assessment of work-related neck and shoulder muscle fatigue is not well established. Therefore, the purpose of this study was to establish DWT analysis as a suitable method to conduct quantitative assessment of neck and shoulder muscle fatigue under dynamic repetitive conditions. Ten human participants performed 40 min of fatiguing repetitive arm and neck exertions while SEMG data from the upper trapezius and sternocleidomastoid muscles were recorded. The ten of the most commonly used wavelet functions were used to conduct the DWT analysis. Spectral changes estimated using power of wavelet coefficients in the 12–23 Hz frequency band showed the highest sensitivity to fatigue induced by the dynamic repetitive exertions. Although most of the wavelet functions tested in this study reasonably demonstrated the expected power trend with fatigue development and recovery, the overall performance of the “Rbio3.1” wavelet in terms of power estimation and statistical significance was better than the remaining nine wavelets.     

Non-invasive diagnosis methods of coronary disease based on wavelet denoising and sound analyzing

The heart sound is the characteristic signal of cardiovascular health status. The objective of this project is to explore the correlation between Wavelet Transform and noise performance of heart sound and the adaptability of classifying heart sound using bispectrum estimation. Since the wavelet has multi-scale and multi-resolution characteristics, in this paper, the heart sound signal with different frequency ranges is decomposed through wavelet and displayed on different scales of the resolving wavelet result. According to distribution features of frequency of heart sound signals, the interference components in heart sound signal can be eliminated by selecting reconstruction coefficients. Comparing de-noising effects of four wavelets which are haar, db6, sym8 and coif6, the db6 wavelet has achieved an optimal denoising effect to heart sound signals. The de-noising result of contrasting different layers in the db6 wavelet shows that decomposing with five layers in db6 provide the optimal performance. In practice, the db6 wavelet also shows commendable denoising effects when applying to 51 clinical heart signals. Furthermore, through the clinic analyses of 29 normal signals from healthy people and 22 abnormal heart signals from coronary heart disease patients, this method can fairly distinguish abnormal signals from normal signals by applying bispectrum estimation to denoised signals via ARMA coefficients model.     

Investigating the Effect of Flickering Frequency Pair and Mother Wavelet Selection in Steady-State Visually-Evoked Potentials on Two-Command Brain-Computer Interfaces

IntroductionSteady-state visually evoked potentials (SSVEPs) have become popular in brain-computer interface (BCI) applications in addition to many other applications on clinical neuroscience (neurodegenerative disorders, schizophrenia, epilepsy, etc.), cognitive (visual attention, working memory, brain rhythms, etc.), and use of engineering researches. Among available methods to measure brain activities, SSVEPs have advantages like higher information transfer rate, simplicity in structure, and short training time. SSVEP-based BCIs use flickering stimuli at different frequencies to discriminate distinct commands in real life. Some features are extracted from the SSVEP signals before these commands are classified. The wavelet transform (WT) has attracted researchers among feature extraction methods since it utilizes the non-stationary signals well. In the WT, a sample function (named mother wavelet) represents the SSVEP signal in both time and frequency domains. Unfortunately, there is no universal mother wavelet function that fits all the signals. Therefore, choosing an appropriate mother wavelet function may be a challenge in WT-related studies. Although there are such studies in three- and seven-command SSVEP-based studies, there is no study for two-command systems in our knowledge.Materials and MethodsIn this study, two user commands flickered at the combinations of seven different frequencies were tested to determine which frequency pairs give the highest performance. For this purpose, three well-known wavelet features (energy, entropy, and variance) were calculated for each of derived EEG frequency bands from the discrete WT coefficients of SSVEP signals. The WT was repeated for six different mother wavelet functions (Haar, Db4, Sym4, Coif1, Bior3.5, and Rbior2.8). Then, four feature sets (every three features, and all together) were applied to seven commonly-used machine learning algorithms (Decision Tree, Discriminant Analysis, Logistic Regression, Naive Bayes, Support Vector Machines, Nearest Neighbors, and Ensemble Classifiers).Results and DiscussionWe achieved 100% accuracies among these 3,528 runs (7 classifiers x 4 feature sets x 6 mother wavelets x 21 flickering frequency pairs) using the mother wavelet function of Haar and the Ensemble Learner classifier. The highest classifier performances are 100% when two commands have the flickering frequency pairs of (6.0 and 10 Hz), (6.5 and 8.2 Hz), or (6.5 and 10.0 Hz).ConclusionWe obtained three main outcomes from this study. First, the most representative mother wavelet function was Haar, while the worst one was Symlet 4. Second, the Ensemble Learner classifier gave the maximum classifier performance in a two-command SSVEP-based BCI system. Besides, two user commands from SSVEP should be one of the frequency pairs of (6.0 and 10.0 Hz), (6.5 and 8.2 Hz), and (6.5 and 10.0 Hz) to achieve the maximum accuracy.     

肌肉动态收缩期间表面肌电信号的时频分析

介绍了用于肌肉动态收缩期间非平稳表面肌电信号的时频分析方法。用短时傅里叶变换、Wigner-Ville分布及Choi-Williams分布计算了表面肌电信号的时频分布,用于信号频率内容随时间演化的可视化观察。通过计算瞬时频谱参数,对肌肉疲劳的电表现进行量化描述。分析了反复性的膝关节弯曲和伸展运动期间从股外侧肌所记录的表面肌电信号。发现和在静态收缩过程中观察到的平均频率线性下降不同,在动态收缩期间瞬时平均频率的变化过程是非线性的并且更为复杂,且与运动的生物力学条件有关。研究表明将时频分析技术应用于动态收缩期间的表面肌电信号可以增加用传统的频谱分析技术不能得到的信息。     

Assessment of wavelet analysis of gait in children with typical development and cerebral palsy

The objective of this study was to examine the use of the continuous wavelet transform (CWT) on surface electromyographic (sEMG) signals acquired from the lower extremity muscles during gait in children with typical development (TD) and cerebral palsy (CP). This was done to explore the possibility of developing a quantitative assessment scale of motor function based on time-frequency information. An initial study was conducted on retrospective gait data from three children, matched in gender and in anthropometric variables but with differing levels of walking ability. EMG data were extracted from five lower extremity muscles to assess the degrees of differentiation. The data were processed using the CWT to derive an average scalogram, from which the instantaneous mean frequency (IMNF) was calculated. Principal component analysis was used to assess the differences between the curves. Preliminary results indicated that for select lower extremity muscles, there was a significant deviation in the IMNF curves in the child with CP as compared to the child with TD. Furthermore, as motor impairment increased, total percent explained variance to the TD curves decreased. This suggests that it might be possible to derive a physiologically based quantitative index for assessing motor function and for assessing clinical treatments in CP using the wavelet analysis.     

Wavelet Representation of the Corneal Pulse for Detecting Ocular Dicrotism

Purpose

To develop a reliable and powerful method for detecting the ocular dicrotism from non-invasively acquired signals of corneal pulse without the knowledge of the underlying cardiopulmonary information present in signals of ocular blood pulse and the electrical heart activity.

Methods

Retrospective data from a study on glaucomatous and age-related changes in corneal pulsation [PLOS ONE 9(7),(2014):e102814] involving 261 subjects was used. Continuous wavelet representation of the signal derivative of the corneal pulse was considered with a complex Gaussian derivative function chosen as mother wavelet. Gray-level Co-occurrence Matrix has been applied to the image (heat-maps) of CWT to yield a set of parameters that can be used to devise the ocular dicrotic pulse detection schemes based on the Conditional Inference Tree and the Random Forest models. The detection scheme was first tested on synthetic signals resembling those of a dicrotic and a non-dicrotic ocular pulse before being used on all 261 real recordings.

Results

A detection scheme based on a single feature of the Continuous Wavelet Transform of the corneal pulse signal resulted in a low detection rate. Conglomeration of a set of features based on measures of texture (homogeneity, correlation, energy, and contrast) resulted in a high detection rate reaching 93%.

Conclusion

It is possible to reliably detect a dicrotic ocular pulse from the signals of corneal pulsation without the need of acquiring additional signals related to heart activity, which was the previous state-of-the-art. The proposed scheme can be applied to other non-stationary biomedical signals related to ocular dynamics.     

Wavelet analysis of frequency chaos game signal: a time-frequency signature of the <Emphasis Type="Italic">C. elegans</Emphasis> DNA

Challenging tasks are encountered in the field of bioinformatics. The choice of the genomic sequence’s mapping technique is one the most fastidious tasks. It shows that a judicious choice would serve in examining periodic patterns distribution that concord with the underlying structure of genomes. Despite that, searching for a coding technique that can highlight all the information contained in the DNA has not yet attracted the attention it deserves. In this paper, we propose a new mapping technique based on the chaos game theory that we call the frequency chaos game signal (FCGS). The particularity of the FCGS coding resides in exploiting the statistical properties of the genomic sequence itself. This may reflect important structural and organizational features of DNA. To prove the usefulness of the FCGS approach in the detection of different local periodic patterns, we use the wavelet analysis because it provides access to information that can be obscured by other time-frequency methods such as the Fourier analysis. Thus, we apply the continuous wavelet transform (CWT) with the complex Morlet wavelet as a mother wavelet function. Scalograms that relate to the organism Caenorhabditis elegans (C. elegans) exhibit a multitude of periodic organization of specific DNA sequences.     

Soft-output signal detection for cetacean vocalizations using spectral entropy,k-means clustering and the continuous wavelet transform

Underwater passive acoustic monitoring systems record many hours of audio data for marine research, making fast and reliable non-causal signal detection paramount. Such detectors assist in reducing the amount of labor required for signal annotations, which often contain large portions devoid of signals.Cetacean vocalization detection based on spectral entropy is investigated as a means of vocalization discovery. Previous techniques using spectral entropy mostly consider time–frequency enhancement of the entropy measure, and utilize the short time Fourier transform (STFT) as its time–frequency (TF) decomposition. Spectral entropy methods also requires the user to set a detection threshold manually, which call for knowledge of the produced entropy measures.This paper considers median filtering as a simple, effective way to provide temporal stabilization to the entropy measure, and considers the continuous wavelet transform (CWT) as an alternative TF decomposition. K-means clustering is used to determine the threshold required to accurately separate the signal/no-signal entropy measures, resulting in a one-dimensional, two-class classification problem. The class means are used to perform pseudo-probabilistic soft class assignment, which is a useful metric in algorithmic development. The effect of median filtering, signal-to-noise ratio and the chosen TF decomposition are investigated.The accuracy and specificity measures of the proposed detection technique are simulated using a pulsed frequency modulated sweep, corrupted by a sample of ocean noise. The results show that median filtering is particularly effective for low signal-to-noise ratios. Both the STFT and CWT prove to be effective TF analyses for signal detection purposes, each presenting with different advantages and drawbacks. The simulated results provide insight into configuring the proposed detector, which is compared to a conventional STFT-based spectral entropy detector using manually annotated humpback whale (Megaptera novaeangliae) songs recorded in False Bay, South Africa, July2021.The proposed method shows a significant improvement in detection accuracy and specificity, while also providing a more interpretable detection threshold setting via soft class assignment, providing a detector for use in development of adaptive algorithms.     

诱发电位的多通道时频相干提取算法

多通道时频域相干成分提取算法是针对低信噪比的宽频带信号提取问题提出的。它采用多通道同步观测,在各通道的观测数据中信号成分具有较高的相干性,而噪声的相干性较低,因此根据其相干性的高低差别即可将信号与噪声分离,提取有效信号。为实现信号与噪声的分离,首先应用小波包分解将信号在时频域展开,然后通过计算相干系数确定信号的时频分布,最终通过小波包重构将信号从噪声中分离出来。这一算法不需要信号的任何先验知识,收敛快,可以有效地提取宽频带信号,极大地提高信号的信噪比,对非重复性信号具有良好的捕捉能力．应用此算法成功地实现了视觉诱发电位的单次提取。     

A generating model of realistic synthetic heart sounds for performance assessment of phonocardiogram processing algorithms

A new model which is capable of generating realistic synthetic phonocardiogram (PCG) signals is introduced based on three coupled ordinary differential equations. The new PCG model takes into account the respiratory frequency, the heart rate variability and the time splitting of first and second heart sounds. This time splitting occurs with each cardiac cycle and varies with inhalation and exhalation. Clinical PCG statistics and the close temporal relationship between events in ECG and PCG are used to deduce values of PCG model parameters.In comparison with published PCG models, the proposed model allows a larger number of known PCG features to be taken into consideration. Moreover it is able to generate both normal and abnormal realistic synthetic heart sounds. Results show that these synthetic PCG signals have the closest features to those of a conventional heart sound in both time and frequency domains. Additionally, a sound quality test carried out by eight cardiologists demonstrates that the proposed model outperforms the existing models.This new PCG model is promising and useful in assessing signal processing techniques which are developed to help clinical diagnosis based on PCG.     

Time-frequency analysis and filtering of kinematic signals with impacts using the Wigner function: accurate estimation of the second derivative

Biomechanical signals are represented in the time-frequency domain using the Wigner distribution function. Filtering of this representation for the case of a non-stationary displacement signal with impact is studied. Smoothed displacement data are then double differentiated and compared with references accelerometer data. It is shown that this technique is able to remove noise from these signals in a better way than conventional filtering techniques currently used in biomechanics.     

Influence of very low doses of mediators on fungal laccase activity - nonlinearity beyond imagination

Background  

Compared 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.     

Wavelet analysis of nonstationary fluctuations of Monte Carlo-simulated excitatory postsynaptic currents

Tracking spectral changes of rapidly varying signals is a demanding task. In this study, we explore on Monte Carlo-simulated glutamate-activated AMPA patch and synaptic currents whether a wavelet analysis offers such a possibility. Unlike Fourier methods that determine only the frequency content of a signal, the wavelet analysis determines both the frequency and the time. This is owing to the nature of the basis functions, which are infinite for Fourier transforms (sines and cosines are infinite), but are finite for wavelet analysis (wavelets are localized waves). In agreement with previous reports, the frequency of the stationary patch current fluctuations is higher for larger currents, whereas the mean-variance plots are parabolic. The spectra of the current fluctuations and mean-variance plots are close to the theoretically predicted values. The median frequency of the synaptic and nonstationary patch currents is, however, time dependent, though at the peak of synaptic currents, the median frequency is insensitive to the number of glutamate molecules released. Such time dependence demonstrates that the "composite spectra" of the current fluctuations gathered over the whole duration of synaptic currents cannot be used to assess the mean open time or effective mean open time of AMPA channels. The current (patch or synaptic) versus median frequency plots show hysteresis. The median frequency is thus not a simple reflection of the overall receptor saturation levels and is greater during the rise phase for the same saturation level. The hysteresis is due to the higher occupancy of the doubly bound state during the rise phase and not due to the spatial spread of the saturation disk, which remains remarkably constant. Albeit time dependent, the variance of the synaptic and nonstationary patch currents can be accurately determined. Nevertheless the evaluation of the number of AMPA channels and their single current from the mean-variance plots of patch or synaptic currents is not highly accurate owing to the varying number of the activatable AMPA channels caused by desensitization. The spatial nonuniformity of open, bound, and desensitized AMPA channels, and the time dependence and spatial nonuniformity of the glutamate concentration in the synaptic cleft, further reduce the accuracy of estimates of the number of AMPA channels from synaptic currents. In conclusion, wavelet analysis of nonstationary fluctuations of patch and synaptic currents expands our ability to determine accurately the variance and frequency of current fluctuations, demonstrates the limits of applicability of techniques currently used to evaluate the single channel current and number of AMPA channels, and offers new insights into the mechanisms involved in the generation of unitary quantal events at excitatory central synapses.