Synthesis of nonlinear circuits in time-frequency domain

ABSTRACT In this thesis, the modelling and the circuit implementation of nonlinear dynamical systems have been accomplished from the given time-frequency domain specifications. After the synthesis of the signal from the time-frequency domain energy distribution using either wavelet atom or wavelet ridges method, the dynamical wavelet network has been proposed from the synthesized signal. Then, the circuit of the dynamical wavelet network has been implemented using the newly proposed sigmoidal and Mexican Hat mother wavelet circuits. Finally, the wavelet ridges of the wavelet network output have been calculated by the new ridge determination algorithm based on singular value decomposition in order to compare with the given time-frequency domain specifications. Keywords: Nonlinear dynamical systems, chaos, time-series embedding, time-series modelling, time-frequency distributions, wavelet theory, wavelet network, the circuit implementation of sigmoidal and Mexican hat mother wavelet.