Time-frequency Plots Research Articles

Effect of tightening torque on transducer dynamics and bond strength in wire bonding

This study seeks to quantify the screw-fastening effect of the tool/transducer on wire bonding performance. Aluminum wire bonding experiments were performed on a laboratory test bench. Characterizations of bonding process through a wavelet analysis were used to study the relation between screw fastening, vibration behaviors and bond strength. The time–frequency plots were depicted for identifying un-modeled wire bonding dynamics. Finally some statistically time domain features were presented for further analysis.

Wire bonding dynamics monitoring by wavelet analysis

Aluminum wire bonding was performed on a lab test-bed with PZT transducer device. Vibration behavior of bonder transducer was monitored, and the correlations between bonding pressure, high frequency tool vibrations, and average bond strength were then demonstrated to determine the statistically significant differences among them. Wavelet decomposing, combined with statistics-based data processing, was utilized to explore the details of bonding process and evade inherent bonding uncertainties. Experimental results show that the method is practical and effective even if the interactions between transducer and its bonding target are very small. The obtained time-frequency plots were depicted for identifying un-modeled wire bonding dynamics.

Application of atomic decomposition to gear damage detection

Atomic decomposition can represent arbitrary signals in an overcomplete dictionary sparsely and adaptively, and it can match the local structure of signals very well. Therefore, it possesses advantages over traditional basis-expansion-based signal analysis methods, in extracting characteristic waveforms from complicated mechanical vibration signals. Periodic impulses characterize damaged gear vibration. In order to extract the transient features of gear vibration, atomic decomposition methods, including method of frames (MOF), best orthogonal basis (BOB), matching pursuit (MP) and basis pursuit (BP), are used in the analysis of vibration signals from both healthy and faulty gearboxes. With a compound dictionary specially designed to match the local structure of signals, the meshing frequency and its harmonics, impulses and transient phenomena of the damaged gear vibration signals are extracted simultaneously. Furthermore, from the time–frequency plots of atomic decomposition, the gear tooth damage is recognized easily according to the periodic impulses. By comparing with traditional time–frequency analysis methods, e.g. short time Fourier transform and continuous wavelet transform, it is found that atomic decomposition is more effective in simultaneously extracting the impulses and harmonic components of damaged gear vibration signals.

The spatial distribution and temporal dynamics of brain regions activated during the perception of object and non-object patterns

Both animal and human studies suggest that the efficiency with which we are able to grasp objects is attributable to a repertoire of motor signals derived directly from vision. This is in general agreement with the long-held belief that the automatic generation of motor signals by the perception of objects is based on the actions they afford. In this study, we used magnetoencephalography (MEG) to determine the spatial distribution and temporal dynamics of brain regions activated during passive viewing of object and non-object targets that varied in the extent to which they afforded a grasping action. Synthetic Aperture Magnetometry (SAM) was used to localize task-related oscillatory power changes within specific frequency bands, and the time course of activity within given regions-of-interest was determined by calculating time–frequency plots using a Morlet wavelet transform. Both single subject and group-averaged data on the spatial distribution of brain activity are presented. We show that: (i) significant reductions in 10–25 Hz activity within extrastriate cortex, occipito-temporal cortex, sensori-motor cortex and cerebellum were evident with passive viewing of both objects and non-objects; and (ii) reductions in oscillatory activity within the posterior part of the superior parietal cortex (area Ba7) were only evident with the perception of objects. Assuming that focal reductions in low-frequency oscillations (< 30 Hz) reflect areas of heightened neural activity, we conclude that: (i) activity within a network of brain areas, including the sensori-motor cortex, is not critically dependent on stimulus type and may reflect general changes in visual attention; and (ii) the posterior part of the superior parietal cortex, area Ba7, is activated preferentially by objects and may play a role in computations related to grasping.

Early recognition of regional cardiac ischemia using a 3-axis accelerometer sensor

Perioperative mortality in coronary artery bypass grafting is usually caused by reduced left ventricular function due to regional myocardial ischemia or infarction. Post-operative graft occlusion is a well-known problem in coronary surgery. A sensitive tool to detect graft occlusion and monitor myocardial function may give the opportunity to revise malfunctioning grafts before departure from the hospital. This paper describes how a new method can detect cardiac ischemia using a 3-axis piezoelectric accelerometer. In three anesthetized pigs, a 3-axis piezoelectric accelerometer was sutured on the lateral free wall of the left ventricle. The left anterior descending (LAD) was occluded for different time periods and the accelerometer data were sampled with a PC. Short-time Fourier transform was calculated based on the accelerometer time series. The results were visualized using a 2D color-coded time–frequency plot. In the area of occlusion, a change to stronger power of higher harmonics was observed. Consequently, a difference value between the instant frequency pattern and a reference frequency pattern showed a rise in absolute value during the occlusion period. The preliminary results indicate that early recognition of regional cardiac ischemia is possible by analyzing accelerometer data acquired from the three animal trials using the prototype 3-axis accelerometer sensor.

Analysis and modeling of broadband airgun data influenced by nonlinear internal waves

To investigate acoustic effects of nonlinear internal waves, the two southwest tracks of the SWARM 95 experiment are considered. An airgun source produced broadband acoustic signals while a packet of large nonlinear internal waves passed between the source and two vertical linear arrays. The broadband data and its frequency range (10-180 Hz) distinguish this study from previous work. Models are developed for the internal wave environment, the geoacoustic parameters, and the airgun source signature. Parabolic equation simulations demonstrate that observed variations in intensity and wavelet time-frequency plots can be attributed to nonlinear internal waves. Empirical tests are provided of the internal wave-acoustic resonance condition that is the apparent theoretical mechanism responsible for the variations. Peaks of the effective internal wave spectrum are shown to coincide with differences in dominant acoustic wavenumbers comprising the airgun signal. The robustness of these relationships is investigated by simulations for a variety of geoacoustic and nonlinear internal wave model parameters.

Investigation of peak frequencies in the flopping regime with a two-cylinder array

The variation of the base pressure coefficient ( C p ), velocity power spectra, and velocity time–frequency plots for an array of two cylinders aligned normal to the flow are presented. Power spectra of the fluctuating velocity downstream of the two-cylinder array with s/ d=0.750 (where s is the spacing between the top and bottom surfaces of adjacent cylinders and d is the diameter of the cylinder) show two peaks. The corresponding Wigner–Ville frequency–time plot of the same fluctuating velocity time series shows that the peak frequency observed during a narrow wake remains constant and relatively high while the peak frequency observed during a wide wake remains constant and relatively low. The two frequency values are consistent with the peaks observed in the power spectra. Thus, during flopping, the high frequency observed in the velocity power spectra is always the peak frequency for a narrow wake and the low frequency observed in the velocity power spectra is always the peak frequency for a wide wake.

Fine structure of the low-frequency spectra of heart rate and blood pressure.

BackgroundThe aim of this study was to explore the principal frequency components of the heart rate and blood pressure variability in the low frequency (LF) and very low frequency (VLF) band. The spectral composition of the R–R interval (RRI) and systolic arterial blood pressure (SAP) in the frequency range below 0.15 Hz were carefully analyzed using three different spectral methods: Fast Fourier transform (FFT), Wigner-Ville distribution (WVD), and autoregression (AR). All spectral methods were used to create time–frequency plots to uncover the principal spectral components that are least dependent on time. The accurate frequencies of these components were calculated from the pole decomposition of the AR spectral density after determining the optimal model order – the most crucial factor when using this method – with the help of FFT and WVD methods.ResultsSpectral analysis of the RRI and SAP of 12 healthy subjects revealed that there are always at least three spectral components below 0.15 Hz. The three principal frequency components are 0.026 ± 0.003 (mean ± SD) Hz, 0.076 ± 0.012 Hz, and 0.117 ± 0.016 Hz. These principal components vary only slightly over time. FFT-based coherence and phase-function analysis suggests that the second and third components are related to the baroreflex control of blood pressure, since the phase difference between SAP and RRI was negative and almost constant, whereas the origin of the first component is different since no clear SAP–RRI phase relationship was found.ConclusionThe above data indicate that spontaneous fluctuations in heart rate and blood pressure within the standard low-frequency range of 0.04–0.15 Hz typically occur at two frequency components rather than only at one as widely believed, and these components are not harmonically related. This new observation in humans can help explain divergent results in the literature concerning spontaneous low-frequency oscillations. It also raises methodological and computational questions regarding the usability and validity of the low-frequency spectral band when estimating sympathetic activity and baroreflex gain.

Topographic Time-Frequency Decomposition of the EEG

Frequency-transformed EEG resting data has been widely used to describe normal and abnormal brain functional states as function of the spectral power in different frequency bands. This has yielded a series of clinically relevant findings. However, by transforming the EEG into the frequency domain, the initially excellent time resolution of time-domain EEG is lost. The topographic time-frequency decomposition is a novel computerized EEG analysis method that combines previously available techniques from time-domain spatial EEG analysis and time-frequency decomposition of single-channel time series. It yields a new, physiologically and statistically plausible topographic time-frequency representation of human multichannel EEG. The original EEG is accounted by the coefficients of a large set of user defined EEG like time-series, which are optimized for maximal spatial smoothness and minimal norm. These coefficients are then reduced to a small number of model scalp field configurations, which vary in intensity as a function of time and frequency. The result is thus a small number of EEG field configurations, each with a corresponding time-frequency (Wigner) plot. The method has several advantages: It does not assume that the data is composed of orthogonal elements, it does not assume stationarity, it produces topographical maps and it allows to include user-defined, specific EEG elements, such as spike and wave patterns. After a formal introduction of the method, several examples are given, which include artificial data and multichannel EEG during different physiological and pathological conditions.

Maximum likelihood approach to image texture and acoustic signal classification

The authors describe a method of classifying natural textures based on the maximum likelihood parameter estimation technique. The novelty of the technique lies in the use of textural features that are derived from the subbands of a wavelet transformed image via the co-occurrence matrices. A maximum likelihood classifier is designed using a set of training texture samples. Ten different Brodotz textures have been classified using this procedure with an average classification accuracy of 99.7%. The main emphasis is to apply this technique to the classification of underwater acoustic signals. A time–frequency plot is obtained for each segment of the acoustic signal and then converted to an intensity pattern. The textural classification scheme is then applied to the intensity patterns of the acoustic signals. Eight different underwater acoustic signals have been classified by this procedure with an average accuracy of 99.99%.

The phase–corrected undecimated discrete wavelet packet transform and its application to interpreting the timing of events

This paper is concerned with the development and application of the phase–corrected maximal overlap discrete wavelet packet transform (MODWPT). The discrete cyclic filtering steps of the MODWPT are fully explained. Energy preservation is proven. With filter coefficients chosen from Daubechie's least asymmetric class, the optimum time shifts to apply to ensure approximate zero phase filtering at every level of the MODWPT are studied, and applied to the wavelet packet coefficients to give phase corrections which ensure alignment with the original time series. Also, the time series values at each time are decomposed into details associated with each frequency band, and these line up perfectly with features in the original time series since the details are shown to arise through exact zero phase filtering. The phase–corrected MODWPT is applied to a non–stationary time series of hourly averaged Southern Hemisphere solar magnetic field magnitude data acquired by the Ulysses spacecraft. The occurrence times of the shock waves previously determined via manual pattern matching on the raw data match those times in the time–frequency plot where a broadband spectrum is obtained; in other words, the phase–corrected MODWPT provides an approach to picking the location of complicated events. We demonstrate the superiority of the MODWPT in interpreting timing information over two competing methods, namely the cosine packet transform (or ‘local cosine transform’), and the short–time Fourier transform.

Slow oscillations of cytochrome oxidase redox state and blood volume in unanesthetized cat and rabbit cortex. Interhemispheric synchrony.

The purpose of this study was to determine the frequency characteristics and the degree of interhemispheric synchrony of slow (< 0.5 Hz), spontaneous oscillations of the regional cortical cytochrome oxidase redox state (CYT) and blood volume (CBV) in unanesthetized animals. We implanted bilateral cortical windows and electrodes for polysomnography in 7 cats and 3 rabbits. The animals were atraumatically restrained during multiple 3-6 hour sessions for up to 8 weeks, and relative changes in the cortical CYT and CBV were monitored by dual wavelength reflectance spectrophotometry at 603 nm and 590 nm. Continuous oscillations of CYT and CBV, unrelated to pulse or respiration, were always observed in each animal. Frequency (FFT) analysis over time revealed a nonstationary distribution of frequencies below 0.4 Hz, with most of the spectral power being contained in the 0-0.25 Hz band during both waking and sleep. Although the time-frequency plots of the CYT and CBV signals were similar, an occasional dissociation between the CYT and CBV oscillations was found. Analysis of simultaneous bilateral cortical optical recordings revealed a significant and sustained interhemispheric cross-correlation over time between the CYT as well as the CBV oscillations during stable recordings as long as 60 min. We conclude that: 1) CYT and CBV levels normally oscillate at < 0.4 Hz in the unanesthetized cat and rabbit cortex; 2) these complex oscillations, whose frequencies are non-stationary over time, nevertheless show sustained interhemispheric synchrony between 50 mm2 homotopic cortical regions; and 3) these oscillations may in part represent fluctuations of the metabolic rate.

Effect of Cage Size on Ultradian Locomotor Rhythms of Laboratory Mice

POON, A. M. S., B. M. WU, P. W. F. POON, E. P. W. CHEUNG, F. H. Y. CHAN AND F. K. LAM. Effect of cage size on ultradian locomotor rhythms of laboratory mice. PHYSIOL BEHAV 62(6) 1253–1258, 1997.—The effect of cage size on spontaneous locomotor rhythms of laboratory mice was studied under simulated light–dark (12:12) cycles. On-line image analysis of bodily displacement yielded a locomotor signal over a period of 3 days. Continuous wavelet transform was applied to the signal, and ensemble averaging of eight mice revealed in the time–frequency plot bouts of increased motor activities. Notably, there were two bouts in the dark corresponding to ultradians of periods below 5 h: a first bout at the dark onset (at 0.6–1.0 cycle/h), and a second bout during the second half of the dark period (at 0.4–0.7 cycle/h). These increases of activity were more intense and distinct when the animals were kept inside the larger cage. Furthermore, the first bout disappeared when the animals were kept in the small cage for 3 days.

Application of NORDEN transform to time-frequency characterization of time-varying signals

The non-orthodox decomposition (NORDEN) transform developed by NASA [N. Huang et al., ‘‘The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Nonstationary Time Series Analysis’’ (to be published)] is designed to adaptively break down a complex time-varying signal into a sum of several simple mode functions. Each single mode function can then be expressed in terms of an analytic signal whose amplitude and phase vary with time and can be displayed as a trace in a time frequency plot, the VEIN diagram, with magnitude expressed as line thickness or color coded. This methodology of signal analysis, unlike other traditional transform methods, i.e., Fourier, Wigner-Ville, and Wavelet, requires no special window, preselected kernel, or particularly selected mother wavelet and provides more detailed dynamic information about the signal under study in terms of its dominant components and their instantaneous frequency variation in the observation time. Several examples from various types of acoustic signals are examined with this algorithm to demonstrate its signal analysis capability.

Equatorial Kelvin wave variability during 1992 and 1993

Temperature and ozone data from the Microwave Limb Sounder (MLS) instrument on UARS are used to analyze the variability of Kelvin wave activity during the first two years of the UARS mission. The analysis is carried out using the asynoptic mapping technique. Time frequency plots for zonal wavenumbers 1 and 2, at two heights representing the middle stratosphere and the stratopause, respectively, are used to analyze the temporal variability of the waves, and its possible relationship to the equatorial quasi‐biennial oscillation (QBO) and semiannual oscillation (SAO). Kelvin wave activity reaches a maximum during the solstice seasons and almost disappears during the equinoxes, in agreement with previous studies. Eastward propagating variance is estimated for wave periods from 4 to 20 days, at all UARS pressure surfaces currently available for MLS. The semiannual modulation of variance is observed to extend down to the lower limits of the height ranges of the temperature and ozone retrievals. Furthermore, a superposed QBO modulation is detected up to the stratopause. Comparison between the variance in eastward propagating waves and the mean zonal wind shows a possible participation of kelvin waves in the forcing of the QBO. At the stratopause the role of Kelvin waves in forcing the SAO appears to be limited, in agreement with previous results. Between the 21‐hPa and 4.6‐hPa surfaces there appears to be a transition zone where there is no clear relationship between Kelvin wave activity and mean zonal flow acceleration.

On the shape of (evoked) otoacoustic emission spectra

In a preceding paper [Wit et al., (1994) Hear. Res. 73, 141–147] it was shown that realistic time-frequency plots for click evoked otoacoustic emissions can be synthesized by adding a large number of gammatones. It is necessary in such a synthesis to make the inner ear frequency to place map, from which the central frequencies of the gammatones are taken, slightly irregular along the entire cochlear partition. The present paper shows that this approach leads, in a rather straightforward way, to (quasi-) periodicity in synthesized spectra of evoked otoacoustic emissions. These spectra show good resemblance with spectra from real ear emission measurements.

A comparison between the modified spectrogram and the pseudo-Wigner-Ville distribution with and without modification

Two main factors have previously favoured the choice of the pseudo-Wigner-Ville distribution (PWVD) over the spectrogram for time-frequency analysis of monocomponent signals. First, the PWVD has better resolution, and secondly, it provides a more accurate estimate of the instantaneous frequency. However, Kodera's modification of the spectrogram provides significant improvements in both these areas. The spectrogram's energy can be repositioned closer to the instantaneous frequency, and the spread in time and frequency due to the lag window can be reduced. This paper applies Kodera's modification to the PWVD and demonstrates that the modified PWVD can reduce the small amount of spreading in frequency introduced by the PWVD's time lag window. The performance of the PWVD, the modified spectrogram, and the modified PWVD are compared using time-frequency plots, for a selection of noise-free monocomponent and multicomponent signals. The modified distributions are shown to produce more highly resolved estimates of the instantaneous frequency for the monocomponent signals. The modified spectrogram is particularly useful for multicomponent signals with components that are well separated in time and frequency as it can provide highly resolved individual components without the significant cross terms which are a feature of PWVD.

Automatic classification and analysis of microneurographic spike data using a PC/AT

Using a standard PC-AT with a commercial analog data interface a system was designed which supports microneurographic experiments and which may also be used for other types of extracellular spike recordings. The signal is sampled on-line at 25 kHz and a spike is detected if the signal passes a certain threshold. The spikes are displayed on the screen and stored on disk. A second on-line mode records the responses of the examined unit to electrical stimulations, which are used to identify the type of fibre and to test the subsequent spike classification. The spikes are classified off-line using a template matching algorithm, which has unsupervised learning and discrimination phases. The results are displayed in a time-frequency plot and may be checked with the responses to electrical stimulations. Artifacts from EMG and other electrical fields are reliably sorted out. In recordings, which include more than one unit, their spikes are discriminated with a low error rate.