Morlet Continuous Wavelet Transform Research Articles

Wavelet analysis of valve closing sound detects malfunction of bileaflet mechanical valve

Several studies have reported the asynchronous closure of normal bileaflet valves (NBVs), resulting in a split in its closing sound; however, the clinical significance of this split has never been studied in malfunctioning bileaflet valves (MBVs). The study comprised 218 valves in 184 patients, including normal monoleaflet valves (n = 10), NBVs (n = 198), and MBVs (n = 10). Valve function was confirmed by cinefluoroscopy prior to analysis of the valve sound by the Morlet continuous wavelet transform (CWT). The split interval (SI) for each heartbeat was measured, and the coefficient of variation (CV) of its mean (valve SI) was calculated as a parameter for the fluctuation of the SI. The CWT of monoleaflet valves showed a single spike, whereas NBVs exhibited a clear split. There was no significant difference in valve SI between the aortic and mitral positions; however, the mean of the CV was significantly greater in the mitral position (n = 90, 0.507 +/- 0.254) than in aortic position (n = 108, 0.353 +/- 0.228, P = 0.000045). The split was not found in six (aortic; three, mitral; three) of ten patients with MBVs. The other four patients had a distinct split, but the CV was significantly lower for MBVs (0.138 +/- 0.105) than for NBVs (0.343 +/- 0.221, P = 0.042). Receiver-operating characteristics analysis demonstrated the cutoff line of the CV to be 0.112 for detecting malfunctioning aortic valves with the highest accuracy of 86.1%. This new system using the Morlet CWT can detect MBVs. It will be a useful modality for screening the function of bileaflet valves.

Wavelet analysis of bileaflet mechanical valve sounds

It has been reported that asynchronous leaflet closure in a bileaflet mechanical valve causes a split in the valve closing sound. We have previously reported that the continuous wavelet transform (CWT) with the Morlet wavelet as modified by Ishikawa (the Morlet wavelet) is the most suitable method among the CWTs for detecting a split in the bileaflet mechanical valve sound because this method can detect the highest frequency signal among the CWT methods with higher time resolution. This is the first article which discusses the acoustic properties of five types of bileaflet valves using the Morlet CWT. Similar behavior of the valve sound split intervals with wide fluctuations over consecutive heartbeats was found to be the common finding for all the bileaflet valves. This result suggests that fluctuation of the split interval proves the normal movement of both leaflets without movement disturbance. The mean differences in the split interval between these bileaflet valves were statistically significant, and the wavelet coefficients of the CWT showed characteristic scalographic patterns, such as a teardrop shape or a triangle beneath the split. However, these two findings gave no valuable information for the diagnosis of bileaflet valve malfunction. A split in the valve closing sound with a fluctuating interval was the common finding in these five normally functioning bileaflet valves, and careful observation of the split's behavior may be a key to diagnosis of bileaflet valve malfunction.

Bileaflet mechanical valve sound analysis using a continuous wavelet transform

Bileaflet mechanical valve closing sounds have splits, the duration of which is not constant in normally functioning valves. However, no reports have discussed the influences of valve malfunction on the split interval, neither have any studies discussed the fact that mechanical valve closing sound signals must be analyzed using a time-frequency analysis because they are nonstationary signals. The continuous wavelet transform (CWT), a time-frequency analyzing method using mother wavelets modified by scale numbers, was selected in this study for analyzing bileaflet valve closing sounds because it is easy to understand and has no limitations such as the cross-terms in the Wigner-Ville distribution or the tradeoff between time and frequency resolutions of the short-time Fourier transform. This study compares the properties of the mother wavelets of various CWTs and selects one that is suitable for detection of the clear split in bileaflet mechanical valve closing sound signals. This article also establishes a standard frequency analyzing system for bileaflet mechanical valve sounds. A preliminary study with chirp Doppler signals for comparing the frequency properties of the mother wavelets of various CWTs suggested that Ishikawa's modified Morlet CWT has better time and frequency resolution at the highest frequency scale. Morlet/power CWT analysis of normal in vivo bileaflet valve closing sounds of the ST. Jude Medical (SJM), ATS, and Carbomedics (CM) valves demonstrated clear splits of very short interval at the highest level of frequency. Detection of the disappearance of the split by using this analytical method may be the key to identifying bileaflet mechanical valve malfunction in outpatient departments.

Single-trial detection of human brain responses evoked by laser activation of Aδ-nociceptors using the wavelet transform of EEG epochs

The aim of this study was to identify EEG changes induced by Aδ-nociceptor activation in single trials. In a preliminary experiment, intense CO 2 laser stimuli were delivered to the hand dorsum of five volunteers. The average amplitude of EEG epochs was estimated in the time-frequency (TF) domain using the continuous Morlet wavelet transform (CMT). The result was used as a TF filter enhancing Aδ-nociceptor induced EEG responses. In a second experiment, eight other subjects were delivered laser stimuli with six intensities. The CMT of each EEG epoch was computed. After applying the TF filter, amplitudes within a predefined interval were summed. Whether this sum predicted the occurrence of Aδ-nociceptor activation was tested using the reaction-time to discriminate between Aδ- or C-fibre mediated detection. Results showed that this method accurately identified single-trial EEG responses to Aδ-nociceptor activation.

Damping identification using a continuous wavelet transform: application to real data

A continuous wavelet transform (CWT) based on the Gabor wavelet function is used to identify the damping of a multi-degree-of-freedom system. The common procedures are already known, especially the identification with a Morlet CWT. This study gives special attention to the following: a description of the instantaneous noise, the edge-effect of the CWT, the frequency-shift of the CWT, the bandwidth of the wavelet function and the selection of the parameter σ of the Gabor wavelet function of the CWT. The procedures are demonstrated using several numerical examples and on signals acquired from the lateral vibration of a uniform beam. The study demonstrates the advantages of using the amplitude and phase methods, both of which provide information about the instantaneous noise. The procedures presented are appropriate for automating the identification process.