Complex Hilbert Transform Filter

Hilbert transform is a basic tool in constructing analytical signals for a various applications such as amplitude modulation, envelope and instantaneous frequency analysis, quadrature decoding, shift-invariant multi-rate signal processing and Hilbert-Huang decomposition. This work introduces a complex Hilbert transform (CHT) filter, where the real and imaginary parts are a Hilbert transform pair. The CHT filtered signal is analytic, i.e. its Fourier transform is zero in negative frequency range. The CHT filter is constructed by half-sample delay operators based on the B-spline transform interpolation and decimation procedure. The CHT filter has an ideal phase response and the magnitude response is maximally flat in the frequency range 0 ≤ ω ≤ π. The CHT filter has integer coefficients and the implementation in VLSI requires only summations and register shifts. We demonstrate the feasibility of the CHT filter in reconstruction of the sign modulated CMOS logic pulses in a fibre optic link.