FFT-Based Computation of Shift Invariant Analytic Wavelet Transform

This letter introduces an analytic wavelet transform based on linear phase quadrature mirror filters (QMFs). The computation of the analytic signal and the reconstruction of the signal is carried by the fast Fourier transform (FFT)-based algorithm. The transform yields energy preserving and shift invariant decimated analytic wavelet coefficients, which are free of aliasing effects. The present method can be implemented in the microprocessor and VLSI environment using a commercial FFT chip