Smoothed Pseudo Wigner-Ville Distribution Research Articles

Comparison of gabor-wigner transform and SPWVD as tools of harmonic computation

The measurement algorithms applied in power quality measurement systems are based on Fast Fourier Transformation. That one-dimension frequency analysis is sufficient in many cases. However, to illustrate the character of the signal in a more comprehensive manner, it is crucial to represent the investigated signal on time-frequency plane. There are a lot of time-frequency representations (TFR) for presenting measured signal. The TFR: Short-Time Fourier Transformation (STFT), Smoothed Pseudo Wigner-Ville Distribution (SPWVD) and Gabor-Wigner Transform (GWT) are described in the paper. The ability of implementation of mentioned methods in harmonics computation according to the power quality standards were presented in the paper.

A hybrid time-frequency method based on improved Morlet wavelet and auto terms window

In this paper, a hybrid time-frequency method (HTM) based on the improved Morlet wavelet and auto terms window (ATW) is presented. The Morlet wavelet, for its shape is similar to the mechanical shock signals, is added two parameters which decide the shape of the mother wavelet. The added parameters and the appropriate scale parameter for continuous wavelet transformation (CWT) are calculated using the cross validation method (CVM) and the minimum Shannon entropy method. The useless noise in the original signal can be filtered by the CWT filter de-noising process. An ATW based on the Smoothed Pseudo Wigner–Ville Distribution (SPWVD) spectrum is designed as a window function to suppress the cross terms in Wigner–Ville Distribution (WVD). The gear fault diagnosis experiment results show that the proposed method has a good de-nosing performance and is effective in removing the cross terms and extracting fault feature.

Wind turbine fault diagnosis based on Morlet wavelet transformation and Wigner-Ville distribution

Based on the Morlet wavelet transformation and Wigner-Ville distribution (WVD), we present a wind turbine fault diagnosis method in this paper. Wind turbine can be damaged by moisture absorption, fatigue, wind gusts or lightening strikes. Due to this reason, there is an increasing need to monitor the health of these structures. Vibration analysis is the best-known technology applied in wind turbine condition monitoring, in which the time-frequency analysis techniques such as Wigner-Ville distribution (WVD) are widely used. Theoretically WVD has an infinite resolution in time-frequency domain. For early wind turbine fault signals, however, there are two main difficulties in WVD analysis. One is strong noise signals in the background and the other is cross terms in WVD itself. In this paper, continuous wavelet transformation (CWT) is employed to filter useless noise in raw vibration signals, and auto terms window (ATW) function is used to suppress the cross terms in WVD. In the CWT de-noising process, the Morlet wavelet, whose shape is similar to mechanical shock signals, is chosen to perform CWT on the raw vibration signals. The appropriate scale parameter for CWT is optimized by the cross validation method (CVM). An ATW based on the Smoothed Pseudo Wigner-Ville distribution (SPWVD) spectrum is taken to be a window function to suppress the cross terms in WVD. The new method can not only remove cross terms faraway from the auto terms, but also keep high energy close to every instantaneous frequency, the virtues such as high time-frequency resolution, and good energy aggregation etc. The wind turbine gear fault diagnosis experiment results indicate that the proposed method has a good de-nosing performance and is effective in suppressing the cross terms and extracting fault feature.

Ataxin active site determination using spectral distribution of electron ion interaction potentials of amino acids

Ataxia is a genetic neurological disorder characterised by a neurodegenerative process affecting a motor cortex responsible for balance and coordination. Recently several genes that cause autosomal dominant ataxia development were identified. These abnormal genes share a common ability to produce abnormal ataxin proteins that can affect nerve cells in the cerebellum and spinal cord. Here, using the Resonant Recognition Model (RRM) based on signal processing, we analysed ataxin proteins and identified the characteristic features corresponding to their biological activities. The RRM is a physico-mathematical model developed for analysis of protein interactions. By incorporating Smoothed Pseudo Wigner-Ville distribution (SPWV) in the RRM, we can define the active regions along the protein molecule. The results showed that our computational predictions correspond closely with the experimentally identified locations of the active/binding sites for ataxin-1 and ataxin-3 protein groups. The results obtained provide a valuable insight into the functional performance of ataxin proteins.

Gabor Transform, SPWVD, Gabor-Wigner Transform and Wavelet Transform - Tools For Power Quality Monitoring

The one-dimension frequency analysis based on DFT (Discrete FT ) is sufficient in many cases in detecting power disturbances and evaluating power quality (PQ). To illustrate in a more comprehensive manner the character of the signal, time-frequency analyses are p erformed. The most common known time-frequency representations (TFR) are spectrogram (SPEC) and Gabor Transform (GT). However, the method has a relatively low time-frequency resolution. The other TF R: Discreet Dyadic Wavelet Transform (DDWT), Smoothed Pseudo Wigner-Ville Distribution (SPWVD) and new Gabor-Wigner Transform (GWT) are described in the paper. The main features of the transforms, on the basis of testing signals, are presented.

Endogenous circannual rhythm in luteinizing hormone secretion: insight from signal analysis coupled with mathematical modelling

In sheep, as in many vertebrates, the seasonal pattern of reproduction is timed by the annual photoperiodic cycle, characterized by seasonal changes in the day length. The photoperiodic information is translated into a circadian profile of melatonin secretion. After multiple neuronal relays (within the hypothalamus), melatonin affects gonadotrophin-releasing hormone (GnRH) secretion, which in turn controls ovarian cyclicity. The pattern of GnRH secretion is mirrored by that of luteinizing hormone (LH) secretion, whose plasmatic level can be easily measured. We addressed the question of whether there exists an endogenous circannual rhythm in a tropical sheep (Blackbelly) population that exhibits clear seasonal ovarian activity when ewes are subject to temperate latitudes. We based our analysis on LH time series collected in the course of 3 years from ewes subject to a constant photoperiodic regime. Owing to intra- and interanimal variability and unequal sampling times, the existence of an endogenous rhythm is not straightforward. We have used time-frequency signal processing methods, and especially the smooth pseudo-Wigner-Ville distribution, to extract possible hidden rhythms from the data. To further investigate the low-frequency (LF) and high-frequency (HF) components of the signals, we have designed a simple mathematical model of the LH plasmatic level accounting for the effect of experimental sampling times. The model enables us to (i) confirm the existence of an endogenous circannual rhythm as detected by the LF signal component, (ii) investigate the action mechanism of the photoperiod on the pulsatile pattern of LH secretion (control of the interpulse interval), and (iii) conclude that the HF component is mainly due to the experimental sampling protocol.

Range-Spread Target Detection Based on Cross Time-Frequency Distribution Features of Two Adjacent Received Signals

High resolution radars (HRRs) transmit a wideband signal to achieve a high range resolution. A target is considered as composed of multiple scatterers, which occupy or spread in multiple radar range cells with several scatterers in each cell. Therefore, the reflection of a target spreads in multiple range cells in the received signal, which contains more information of target than that obtained from low resolution radars. The target in high resolution radar systems is a range-spread target. The range-spreading or echo features of target are utilized for target detection and identification. The echoes of target are convolutions of transmitted signals with target range-scattering functions dependent on the gesture of target to the line of radar sight. A single echo is used in the conventional detection. It is difficult for target detection and identification in low signal-to-noise ratio (SNR) condition. In this paper, we propose a new range-spread target detection scheme exploiting the image features of cross time-frequency distribution (TFD) of a pair of adjacent received signals. After dechirping, the received signal reflected from target consists of multiple sinusoidal components due to its multiple scatterers when a linear frequency modulated (LFM) signal is transmitted from radar. Some regular image patterns or features of target appear in the cross TFD of two adjacent received signals, while the cross TFD of two independent Gaussian noises does not show such patterns. The cross TFD features are exploited in the proposed scheme. Three steps are composed in the proposed scheme. Firstly, a cross smoothed-pseudo Wigner-Ville distribution (CSPWVD) is made for two adjacent received signals to generate a two-dimensional (2-D) TF image. Then, some regular geometric patterns are detected and extracted from the image. At last, two features of the extracted geometric patterns are jointly utilized to detect target. The proposed algorithm is verified by using raw radar data. It outperforms the conventional detection methods.

Spectral decomposition of seismic data with reassigned smoothed pseudo Wigner–Ville distribution

Seismic signals are nonstationary mainly due to absorption and attenuation of seismic energy in strata. Referring to spectral decomposition of seismic data, the conventional method using short-time Fourier transform (STFT) limits temporal and spectral resolution by a predefined window length. Continuous-wavelet transform (CWT) uses dilation and translation of a wavelet to produce a time-scale map. However, the wavelets utilized should be orthogonal in order to obtain a satisfactory resolution. The less applied, Wigner–Ville distribution (WVD) being superior in energy distribution concentration, is confronted with cross-terms interference (CTI) when signals are multi-component. In order to reduce the impact of CTI, Cohen class uses kernel function as low-pass filter. Nevertheless it also weakens energy concentration of auto-terms. In this paper, we employ smoothed pseudo Wigner–Ville distribution (SPWVD) with Gauss kernel function to reduce CTI in time and frequency domain, then reassign values of SPWVD (called reassigned SPWVD) according to the center of gravity of the considering energy region so that distribution concentration is maintained simultaneously. We conduct the method above on a multi-component synthetic seismic record and compare with STFT and CWT spectra. Two field examples reveal that RSPWVD potentially can be applied to detect low-frequency shadows caused by hydrocarbons and to delineate the space distribution of abnormal geological body more precisely.

The reassigned local polynomial periodogram and its properties

This paper defines a reassignment method based on the second-order local polynomial periodogram and investigates its properties with some mathematical proofs. Based on simulation results with various signals, such as parallel and crossed chirps, and parabolic and sinusoidal frequency modulated signals, comparisons with the reassigned spectrogram and smoothed pseudo-Wigner–Ville distribution are made to show the desirable ability of the reassigned local polynomial periodogram for improvement on the signal concentration in the time–frequency domain.

On arousal from sleep: time-frequency analysis

Time-frequency analysis of the heart rate variability during arousal from sleep, with and without EMG activation, coming from five obese healthy subjects was performed. Additionally, a comparative analysis of three time-frequency distributions, smooth pseudo Wigner-Ville (SPWVD), Choi-Williams (CWD) and Born-Jordan distribution (BJD) is presented in this study. SPWVD showed higher capacity for eliminating the cross terms independently of the signal. After applying Hilbert transformation to real signals BJD and CWD lost some important mathematic properties as marginals, on the contrary PSWVD remains unchanged. BJD showed results comparable with CWD. During arousal episodes, analogous energy distribution and spectral indexes were obtained by the three time-frequency representations. Arousals with chin activity presented stronger changes in RR intervals and LF (related to sympathetic activity) component, being statistically different with respect to arousal without chin activity, only around the period of maximum change in beta activity on the EEG. These results suggest a more evident stress for the heart when an arousal is related to external muscular activity.

Nonstationary quiver spindle background sound analysis of airplane via Wigner-Ville and wavelet time-scale distribution

Cockpit voice recorder (CVR) in aircraft black box records many cockpit voices, such as speaker voices, noises, special meaning background sounds. Cockpit voices’ complex- ity exacerbates analysis difficulty through traditional differenti- ating hearing methods. These methods’ key techniques puz- zles such as cockpit voices’ characteristics identification are not resolved. According to the shortage in cockpit voice hearing and analyses by traditional Fourier transformation(FT) single time/frequency and short time Fourier transformation (STFT) double energy, the new methods ,which can applied to analysis of no stationary cockpit background sound, is set up by means of introducing Wigner-Ville time-frequency and wavelet time-scale technology respectively into airplane cockpit voice analyses, as an example of quiver spindle background sound recorded by CVR. Compared with these methods, it is demon- strated that the spectrogram of both smooth pseudo Wigner-Ville distribution(SPWVD) and its time-frequency re- distribution features high time-frequency resolution, immunity of cross term interference; and that the resonate frequency and response time are obtained by time-scale analysis of discrete wavelet transformation(DWT) .

Time-Frequency Signal Synthesis and Its Application in Multimedia Watermark Detection

We propose a novel approach to detect the watermark message embedded in images under the form of a linear frequency modulated chirp. Localization of several time-frequency distributions (TFDs) is studied for different frequency modulated signals under various noise conditions. Smoothed pseudo-Wigner-Ville distribution (SPWVD) is chosen and applied to detect and recover the corrupted image watermark bits at the receiver. The synthesized watermark message is compared with the referenced one at the transmitter as a detection evaluation scheme. The correlation coefficient between the synthesized and the referenced chirps reaches 0.9 or above for a maximum bit error rate of 15% under intentional and nonintentional attacks. The method provides satisfactory result for detection of image watermark messages modulated as chirp signal and could be a potential tool in multimedia security applications.

A Signal Processing Module for the Analysis of Heart Sounds and Heart Murmurs

In this paper a Signal Processing Module (SPM) for the computer-aided analysis of heart sounds has been developed. The module reveals important information of cardiovascular disorders and can assist general physician to come up with more accurate and reliable diagnosis at early stages. It can overcome the deficiency of expert doctors in rural as well as urban clinics and hospitals. The module has five main blocks: Data Acquisition & Pre-processing, Segmentation, Feature Extraction, Murmur Detection and Murmur Classification. The heart sounds are first acquired using an electronic stethoscope which has the capability of transferring these signals to the near by workstation using wireless media. Then the signals are segmented into individual cycles as well as individual components using the spectral analysis of heart without using any reference signal like ECG. Then the features are extracted from the individual components using Spectrogram and are used as an input to a MLP (Multiple Layer Perceptron) Neural Network that is trained to detect the presence of heart murmurs. Once the murmur is detected they are classified into seven classes depending on their timing within the cardiac cycle using Smoothed Pseudo Wigner-Ville distribution. The module has been tested with real heart sounds from 40 patients and has proved to be quite efficient and robust while dealing with a large variety of pathological conditions.

Time‐frequency spectral analysis of inspiratory motor discharges during spontaneous and hypoxia‐facilitated augmented (sigh) bursts in anesthetized adult C57BL/6 mice in vivo

Previous work from our laboratory has demonstrated the time-varying (TV) spectral characteristics of eupneic breathing in adult C57BL/6 mice using the Smoothed pseudo-Wigner-Ville distribution (SPWD) method. While temporal (e.g., timing, patterning) differences between the eupneic and augmented (Aug) burst (sigh) patterns have been characterized, the underlying TV spectral characteristics associated with Aug bursts have yet to be examined. Therefore, SPWD analyses were performed on diaphragm EMG bursts recorded from spontaneously breathing urethane-anesthetized adult C57BL/6 mice (n=11) in vivo during eupneic breathing and both spontaneous and hypoxia-facilitated Aug bursts. As previously described, the TV spectrum of eupnea exhibited multiple bursts of spectral activity in the frequency ranges associated with medium (MFO), high (HFO), and upper high (UHFO) frequency oscillations. During Aug bursts, power in the UHFO range was enhanced (P<0.001), spectral duration was reduced, and spectral power was more concentrated; however, there were no shifts in the dominant spectral frequencies. Comparisons between burst pair segments consisting of either two bursts under basal spontaneous (n=159 pairs) or hypoxic (n=42) conditions or an Aug burst and its immediately preceding burst (n=53 spontaneous; n=18 hypoxia-facilitated) revealed that the Aug bursts exhibited increased power relative to the preceding burst (P<0.001), and that this increase in power was more enhanced during the spontaneous Aug bursts as compared to the hypoxia-facilitated Aug bursts (58% spontaneous vs. 67% hypoxia-facilitated). These data support the concept that Aug bursts reflect reconfiguration of the inspiratory neural network. Supported by NS045321

Detection of Induction Motor Faults: A Comparison of Stator Current, Vibration and Acoustic Methods

In this paper we present the comparison results of induction motor fault detection using stator current, vibration, and acoustic methods. A broken rotor bar fault and a combination of bearing faults (inner race, outer race, and rolling element faults) were induced into variable speed three-phase induction motors. Both healthy and faulty signatures were acquired under different speed and load conditions. To address the detection capabilities of the above methods, comparisons are made in both the time and joint time-frequency domains. In the frequency domain, spectral differences are compared and characterized under constant speed conditions. To evaluate the detection sensitivities under non-stationary conditions (e.g. startup), a joint time-frequency method called the smoothed pseudo Wigner-Ville distribution (SPWVD) is employed to analyze non-stationary signatures. The SPWVD is a powerful technique for revealing non-stationary characteristics of motor signatures. Experimental results show that the stator current method is sensitive to the broken rotor bar fault while the vibration method is sensitive to bearing faults. The acoustic method is very attractive in that it contains less noise and interference within the analyzing frequency band. With the proper selection of monitoring and analysis methods, induction motor faults can be detected accurately under both stationary and non-stationary states.

SMOOTHED-PSEUDO WIGNER–VILLE DISTRIBUTION OF NORMAL AND AORTIC STENOSIS HEART SOUNDS

In this paper, we are interested in the acquisition and the time-frequency analysis of the Phonocardiogram (PCG) signal. The interactive software "PCG Recorder" we implemented in MATLAB, drives the sound card of a personal computer for acquisition purposes. Normal and abnormal heart sounds were acquired with 16 bits resolution and at high sampling frequencies; the value 2 kHz was selected as sampling rate to avoid spectral aliasing. For each patient, additional information like the age, the gender, the weight as well as the auscultation area can be introduced within the saved data file. The aortic, the tricuspid, the mitral and the pulmonic areas are considered for the acquisition task. The Smoothed-Pseudo Wigner–Ville Distribution (SPWVD) yield adequate Time-Frequency Representations (TFRs) of such non-stationary signal as heart sounds. Moreover, by taking into account the corresponding auscultation area for each obtained TFR, we adopt exclusion reasoning to attribute each burst to its origins within the myocardium. Furthermore, the alternating functioning of heart valves and cavities in systole and diastole was characterized in the time and frequency domains. Aortic stenosis heart sounds were involved in our study in a view to confirm their pathological nature towards the normal heart sounds findings. Indeed, the weakened S1 and S2 heart sounds and the strong systolic ejection murmur which dominates the overall systole, confirm our hypotheses. Thus, modulations laws relating to the systolic ejection of blood through the stenosed orifice were characterized by means of the reliable SPWVD approach. A third heart sound (S3) which is an indicator of the presence of systolic dysfunction and the elevated filling pressure for aortic stenosis lesion was also characterized.

A 3-D Baseband Signal Analyzer Prototype for 3G Mobile Telecommunication Systems

The paper deals with the realization of a new instrument for the qualification of third-generation (3G) mobile telecommunication systems. It is based on the parallel computing of a time-frequency representation called smoothed pseudo-Wigner-Ville distribution (SPWVD) on a multiple digital signal processor architecture. The SPWVD allows the performance of signal analysis simultaneously in both the time and frequency domain. The hardware and software implementations of the instrument prototype are presented and discussed. Then, the first validation results, obtained on wide-band code-division-multiplexing access (W-CDMA) signals compliant with the 3rd Generation Partnership Program (3GPP) standard, are reported.

Time-Frequency Representation of Inspiratory Motor Output in Anesthetized C57BL/6 Mice In Vivo

Inspiratory motor discharges, in addition to long-time-scale rhythmic oscillatory bursting, exhibit short-time-scale rhythmic oscillations that have been identified, and subsequently characterized, using power spectral analyses [predominantly fast-Fourier transforms (FFT)]. These analyses assume that the signal being analyzed is stationary; however, this is not the case for most biological signals, which exhibit varying degrees of nonstationarity. To overcome this limitation, time-frequency methods, which provide not only the frequency content but also information regarding the timing of these fast rhythmic oscillations (i.e., dynamics of spectral activity), should be used. Thus this study was performed to investigate the dynamic or time-varying features of spectral activity in inspiratory motor output. Both conventional time-invariant and time-frequency (time-varying) spectral analysis methods were performed on recordings of diaphragm EMG, phrenic nerve, and hypoglossal nerve discharges obtained from spontaneously breathing urethan-anesthetized adult C57BL/6 mice. Conventional time-invariant spectral analysis using a FFT algorithm revealed three dominant peaks in the power spectrum, which were located at 1) 20-46, 2) 83-149, and 3) 177-227 Hz. Time-frequency spectral analysis using a generalized time-frequency representation (TFR) with the smoothed pseudo-Wigner-Ville distribution (SPWD) kernel confirmed the general location of these spectral peaks, identified additional spectral peaks within the frequency ranges described above, and revealed a time-dependent expression of spectral activity within the inspiratory burst for each of the frequency ranges. Furthermore, this method revealed that 1) little or no spectral activity occurs during the initial portion of the inspiratory burst in any of the frequency ranges identified, 2) transient oscillations in the magnitude of spectral power exist where spectral activity occurs, and 3) total spectral power exhibits an augmenting pattern over the course of the inspiratory burst. These data, which provide the first description of spectral content in inspiratory motor discharges in adult mice, show that both time-invariant and time-varying spectral analysis methods are capable of identifying short-time-scale rhythmic oscillations in inspiratory motor discharge (as expected); however, the dynamic (i.e., timing) features of this oscillatory activity can only be obtained using the time-frequency method. We suggest that time-frequency methods, such as the SPWD, should be used in future studies examining short-time-scale (fast) rhythmic oscillations in inspiratory motor discharges, because additional insight into the neural control mechanisms that participate in inspiratory-phase neuronal and motoneuronal synchronization may be obtained.

A COMPARATIVE STUDY OF ACOUSTIC AND VIBRATION SIGNALS IN DETECTION OF GEAR FAILURES USING WIGNER–VILLE DISTRIBUTION

Vibration analysis is widely used in machinery diagnostics and the Wigner–Ville distribution has also been implemented in many applications in the condition monitoring of machinery. In contrast to previous applications, this paper examines whether acoustic signal can be used effectively to detect the various local faults in gearboxes using the smoothed pseudo-Wigner–Ville distribution. Three types of progressing local faults, broken tooth, gear crack and localised wear, were simulated. The results from acoustic signals were compared with vibration signals. The results suggest that acoustic signals are very affective for the early detection of faults and may provide a powerful tool to indicate the various types of progressing faults in gearboxes.

Time-frequency analysis of HRV for patient withvasovagal syncope

Time-frequency analysis (TFA) is applied to the heart rate variability (HRV) signal for the purpose of observing the dynamical changes of spectral components. Smoothed-pseudo Wigner-Ville distribution (SPWVD) TFA was considered for processing the HRV signal. As a result, SPWVD TFA on HRV signals is shown to be a very effective method for analysing the power spectral density and for observing the time-varying components of HRV signals.