Hilbert Transform Relations
…Each continuous problem (differential equation)
has many discrete approximations (difference equations).
Gilbert Strang (SIAM Review, Vol. 41, 1999, No 1, 135-147)
Bozhan Zhechev
Institute of Computer and Communication Systems, 1113 Sofia
Abstract:
In this paper the Hilbert transform different cases – for continuous, periodic and discrete signals are analyzed. The main attention is paid to the properties of the discrete cyclic transform. The eigenvectors and eigenvalues of this transform, projectors onto the region of the values, pseudoinverse endomorphism, and connections with another variants are found. The properties of the magnitude response of the different Hilbert’s filters are demonstrated.
Keywords: digital signal processing, inverse filtering, bandpass signals, single-sideband modulation, image processing, discrete Fourier Transform (DFT), fast transforms, invariant spaces, pseudoinverse.