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

Abstract

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.