An analytical method for approximating high-order Galerkin solutions

AbstractThe high-order Galerkin procedures for computing forced oscillations of nonlinear systems are generally impractical to apply analytically. In this paper, an analytical method for approximating high-order Galerkin solutions is presented, which is applicable to ordinary differential equations with polynomial nonlinearities. The procedure is restricted to oscillations whose predominant Fourier component is the fundamental; hence subharmonic oscillations may be allowed, whereas superharmonic oscillations are excluded. The approach taken is to consider only the first-order effects of the higher harmonics. An example is given which demonstrates that the accuracy of the method can be quite impressive

Complex Wavelet Transforms with Allpass Filters

Journal PaperComplex discrete wavelet transforms have significant advantages over real wavelet transforms for certain signal processing problems. Two approaches to the implementation of complex wavelet transforms have been proposed earlier. Both approaches require discrete-time allpass systems having approximately linear-phase and (fractional) delay. This paper compares the results when different allpass systems are used. In the earlier work, maximally flat delay allpass systems were used. In this paper, it is shown that an allpass system designed according to the minimax criterion yields improvements for the complex discrete wavelet transforms