Different forms of the Hilbert transform as applied to digital filters and sequences

The paper presents two aspects of the Hilbert transform; first, a unified survey and treatment of the different forms of the Hilbert transform which arise in the study of digital signal processing systems when considering: (a) the frequency-domain relations between the real and imaginary components of the network function of a linear stable digital filter whose impulse response is causal, and (b) the determination of analytic signals associated with periodic waveforms or sequences specified in the time domain. The continuous forms of the Hilbert transform are developed as special cases of the corresponding discrete cases. Secondly, a comparison of two finiteimpulse response (f.i.r.) digital filters for realising the discrete Hilbert transform is made.