Analysis for Jump Phenomena in Random Response of a Duffing Oscillator Using Continuous Wavelet Transform (2nd Report, Analysis by Complex Wavelet Transform)

2011 ◽  
Vol 77 (783) ◽  
pp. 4081-4089
Author(s):  
Shinji TAMURA ◽  
Yoshifumi FUNAKOSHI ◽  
Yuto KATO
Keyword(s):  
Wavelet Transform ◽  
Continuous Wavelet Transform ◽  
Duffing Oscillator ◽  
Continuous Wavelet ◽  
Random Response ◽  
Complex Wavelet Transform ◽  
Jump Phenomena ◽  
Report Analysis ◽  
Complex Wavelet

Instantaneous frequency estimation and representation of the audio signal through Complex Wavelet Additive Synthesis

2014 ◽  
Vol 12 (03) ◽  
pp. 1450030 ◽  
Author(s):  
Jesús Ponce de León ◽  
José Ramón Beltrán ◽  
Fernando Beltrán
Keyword(s):  
Wavelet Transform ◽  
Comparative Study ◽  
Continuous Wavelet Transform ◽  
Instantaneous Frequency ◽  
Audio Signal ◽  
Frequency Resolution ◽  
Continuous Wavelet ◽  
Time Frequency ◽  
Complex Wavelet ◽  
Additive Synthesis

In this work, an improvement of the Complex Wavelet Additive Synthesis (CWAS) algorithm is presented. This algorithm is based on a discrete version of the Complex Continuous Wavelet Transform (CCWT) which analyzes the input signal in a frame-to-frame approach and under variable frequency resolution per octave. After summarizing several Time-Frequency Distributions (TFD), concretely the standard Short Time Fourier Transform (STFT), the Pseudo Wigner–Ville Distribution (PWVD), reassignment and complex wavelets, a comparative study of the accuracy in the instantaneous frequency (IF) estimation is shown. The comparative study includes three different signal processing tools (based on the summarized TFD): the Time-Frequency Toolbox (TFTB) of François Auger, the High Resolution Spectrographic Routines (HRSR) of Sean Fulop and the proposed CWAS algorithm. A set of eight synthetic signals have been analyzed using six different methods: the regular STFT spectrogram, the PWVD, their corresponding reassigned versions, the Nelson crossed spectrum method and finally the Complex Continuous Wavelet Transform (CCWT). Finally, two- and three-dimensional Time-Frequency representations of the IF provided by the CWAS algorithm are presented.

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