A New Fast Approximate Hilbert Transform with Different Applications

Abstract

A new and fast approximate Hilbert transform based on subband decomposition is presented. This new algorithm is called the subband (SB)-Hilbert transform.  The reduction in complexity is obtained for narrow-band signal applications by considering only the band of most energy.  Different properties of the SB-Hilbert transform are discussed with simulation examples.  The new algorithm is compared with the full band Hilbert transform in terms of complexity and accuracy. The aliasing errors taking place in the algorithm are found by applying the Hilbert transform to the inverse FFT (time signal) of the aliasing errors of the SB-FFT of the input signal.  Different examples are given to find the analytic signal using SB-Hilbert transform with a varying number of subbands.  Applications of the new algorithm are given in single-sideband amplitude modulation and in demodulating frequency-modulated signals in communication systems.

Key Words:  Fast Algorithms, Hilbert Transform, Analytic Signal Processing.