Comment on “Time-frequency analysis with the continuous wavelet transform,” by W. Christopher Lang and Kyle Forinash [Am. J. Phys. 66 (9), 794–797 (1998)]

1999 ◽  
Vol 67 (10) ◽  
pp. 934-935 ◽  
Author(s):  
George Treviño ◽  
Edgar L. Andreas
Keyword(s):  
Wavelet Transform ◽  
Frequency Analysis ◽  
Continuous Wavelet Transform ◽  
Continuous Wavelet ◽  
Time Frequency Analysis ◽  
Time Frequency

scholarly journals Time-frequency analysis of the Surge Onset in the Centrifugal Blower

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
Grzegorz Liskiewicz ◽  
Longin Horodko
Keyword(s):  
Wavelet Transform ◽  
Frequency Analysis ◽  
Continuous Wavelet Transform ◽  
Working Condition ◽  
Continuous Wavelet ◽  
Transient Phase ◽  
Centrifugal Blower ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Pressure Signal

Abstract Time frequency analysis of the surge onset was performed in the centrifugal blower. A pressure signal was registered at the blower inlet, outlet and three locations at the impeller shroud. The time-frequency scalograms were obtained by means of the Continuous Wavelet Transform (CWT). The blower was found to successively operate in four different conditions: stable working condition, inlet recirculation, transient phase and deep surge. Scalograms revealed different spectral structures of aforementioned phases and suggest possible ways of detecting the surge predecessors.

scholarly journals A general theory on frequency and time–frequency analysis of irregularly sampled time series based on projection methods – Part 2: Extension to time–frequency analysis

2018 ◽  
Vol 25 (1) ◽  
pp. 175-200 ◽  
Author(s):  
Guillaume Lenoir ◽  
Michel Crucifix
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Frequency Analysis ◽  
Continuous Wavelet Transform ◽  
Background Noise ◽  
Noise Model ◽  
Analysis Tool ◽  
Continuous Wavelet ◽  
Time Frequency Analysis ◽  
Time Frequency

Abstract. Geophysical time series are sometimes sampled irregularly along the time axis. The situation is particularly frequent in palaeoclimatology. Yet, there is so far no general framework for handling the continuous wavelet transform when the time sampling is irregular. Here we provide such a framework. To this end, we define the scalogram as the continuous-wavelet-transform equivalent of the extended Lomb–Scargle periodogram defined in Part 1 of this study (Lenoir and Crucifix, 2018). The signal being analysed is modelled as the sum of a locally periodic component in the time–frequency plane, a polynomial trend, and a background noise. The mother wavelet adopted here is the Morlet wavelet classically used in geophysical applications. The background noise model is a stationary Gaussian continuous autoregressive-moving-average (CARMA) process, which is more general than the traditional Gaussian white and red noise processes. The scalogram is smoothed by averaging over neighbouring times in order to reduce its variance. The Shannon–Nyquist exclusion zone is however defined as the area corrupted by local aliasing issues. The local amplitude in the time–frequency plane is then estimated with least-squares methods. We also derive an approximate formula linking the squared amplitude and the scalogram. Based on this property, we define a new analysis tool: the weighted smoothed scalogram, which we recommend for most analyses. The estimated signal amplitude also gives access to band and ridge filtering. Finally, we design a test of significance for the weighted smoothed scalogram against the stationary Gaussian CARMA background noise, and provide algorithms for computing confidence levels, either analytically or with Monte Carlo Markov chain methods. All the analysis tools presented in this article are available to the reader in the Python package WAVEPAL.

scholarly journals A time–frequency analysis based internal leakage detection method for hydraulic actuators

2017 ◽  
Vol 9 (1) ◽  
pp. 168781401668505 ◽  
Author(s):  
Zhikai Yao ◽  
Jian Tang ◽  
Ting Rui ◽  
Jinhui Duan
Keyword(s):  
Wavelet Transform ◽  
Frequency Analysis ◽  
Continuous Wavelet Transform ◽  
Control Valve ◽  
Experimental Tests ◽  
Continuous Wavelet ◽  
Time Frequency Analysis ◽  
Hydraulic Actuators ◽  
Time Frequency ◽  
Pressure Signal

Internal leakage in the hydraulic actuators is concerned in this article, which is caused by seal damage, resulting in the limited performance of the system. To study the issue, this article proposes a method based on time–frequency analysis for the detection in hydraulic actuators. First, the pressure signal after filtering of the actuator in one side is collected when the control valve is affected by sinusoidal-like inputs. Second, the time–frequency image of pressure signal in a period at different leakage levels is obtained after continuous wavelet transform. Third is the sum of pixels in the time–frequency image. It is shown that the feature pattern is established by the sum of pixels in the time–frequency image that internal leakage and its severity could be detected effectively. The proposed method required two baselines and premeasured the pressure signal at 11 leakage levels. Once the sum of pixels in the time–frequency image values, obtained from the time–frequency image by continuous wavelet transform based on wavelet Cmor1-1 in subsequent offline tests, are greater than the first baseline, a leakage alarm is triggered. Furthermore, a severe leakage alarm is triggered when the value is greater than the second baseline. Experimental tests show the accuracy of the proposed scheme at different mother wavelets, and it is done without knowing the model of actuator or leakage.

scholarly journals Time-frequency analysis on gong timor music using short-time fourier transform and continuous wavelet transform

2017 ◽  
Vol 3 (3) ◽  
pp. 146
Author(s):  
Yovinia Carmeneja Hoar Siki ◽  
Natalia Magdalena Rafu Mamulak
Keyword(s):  
Fourier Transform ◽  
Wavelet Transform ◽  
Frequency Analysis ◽  
Continuous Wavelet Transform ◽  
Continuous Wavelet ◽  
Short Time Fourier Transform ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Music Signal ◽  
Short Time

Time-Frequency Analysis on Gong Timor Music has an important role in the application of signal-processing music such as tone tracking and music transcription or music signal notation. Some of Gong characters is heard by different ways of forcing Gong himself, such as how to play Gong based on the Player’s senses, a set of Gong, and by changing the tempo of Gong instruments. Gong's musical signals have more complex analytical criteria than Western music instrument analysis. This research uses a Gong instrument and two notations; frequency analysis of Gong music frequency compared by the Short-time Fourier Transform (STFT), Overlap Short-time Fourier Transform (OSTFT), and Continuous Wavelet Transform (CWT) method. In the STFT and OSTFT methods, time-frequency analysis Gong music is used with different windows and hop size while CWT method uses Morlet wavelet. The results show that the CWT is better than the STFT methods.

scholarly journals A general theory on frequency and time-frequency analysis of irregularly sampled time series based on projection methods. II. Extension to time-frequency analysis

2017 ◽  
Author(s):  
Guillaume Lenoir ◽  
Michel Crucifix
Keyword(s):  
Time Series ◽  
Wavelet Transform ◽  
Frequency Analysis ◽  
Continuous Wavelet Transform ◽  
Background Noise ◽  
Noise Model ◽  
Analysis Tool ◽  
Continuous Wavelet ◽  
Time Frequency Analysis ◽  
Time Frequency

Abstract. Geophysical time series are sometimes sampled irregularly along the time axis. The situation is particularly frequent in palaeoclimatology. Yet, there is so far no general framework for handling continuous wavelet transform when the time sampling is irregular. Here we provide such a framework. To this end, we define the scalogram as the continuous-wavelet-transform-equivalent of the extended Lomb-Scargle periodogram defined in part I of this study (Lenoir and Crucifix, 2017). The signal being analyzed is modeled as the sum of a locally periodic component in the time-frequency plane, a polynomial trend, and a background noise. The mother wavelet adopted here is the Morlet wavelet classically used in geophysical applications. The background noise model is a stationary Gaussian continuous autoregressive-moving-average (CARMA) process, which is more general than the traditional Gaussian white and red noise processes. The scalogram is smoothed by averaging over neighboring times in order to reduce its variance. The Shannon-Nyquist exclusion zone is on the other hand defined as the area corrupted by local aliasing issues. The local amplitude in the time-frequency plane is then estimated with least-squares methods. We show that the squared amplitude and the scalogram are approximately proportional. Based on this property, we define a new analysis tool: the weighted smoothed scalogram, which we recommend for most analyses. The estimated signal amplitude also gives access to band and ridge filtering. Finally, we design a test of significance for the weighted smoothed scalogram against the stationary Gaussian CARMA background noise, and provide algorithms for computing confidence levels, either analytically or with Monte Carlo Markov Chain methods. All the analysis tools presented in this article are available to the reader in the Python package WAVEPAL.

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