Title :
A parametric modeling approach to Hilbert transformation
Author :
Rao, Ashwin ; Kumaresan, Ramdas
Author_Institution :
Dept. of Electr. Eng., Rhode Island Univ., Kingston, RI, USA
Abstract :
A parametric approach to compute the Hilbert transform (HT) of a real signal is proposed. A scaled version of the real signal is raised to the exponent of Napier´s base, and an all-pole signal model is fitted to approximate the resulting signal as though it were the envelope. An error criterion that flattens this envelope is then minimized over a set of complex Fourier coefficients. The resulting approximation is guaranteed to be a minimum-phase (MinP) signal. Since a MinP signal has the property that the logarithm of its envelope and its phase are related by the HT, it follows that the resulting phase of MinP approximation yields the desired HT.
Keywords :
Hilbert transforms; all-pass filters; approximation theory; filtering theory; parameter estimation; poles and zeros; prediction theory; signal sampling; signal synthesis; spectral analysis; Hilbert transformation; Napier´s base; all-pole signal model; allpass filter; analytic signals; complex Fourier coefficients; discrete-time Hilbert transformers; error criterion; linear prediction in spectral domain; minimum-phase approximation; minimum-phase signal; parametric modeling approach; real signal; sampling frequency; scaled version; signal approximation; sinusoidal signal synthesis; Discrete transforms; Frequency; Narrowband; Parametric statistics; Performance analysis; Sampling methods; Signal analysis; Signal processing; Transformers; Voltage-controlled oscillators;
Journal_Title :
Signal Processing Letters, IEEE
