Optimum masking levels and coefficient sparseness for Hilbert transformers and half-band filters designed using the frequency-response masking technique

Abstract

Hilbert transformers and half-band filters are two very important special classes of finite-impulse response filters often used in signal processing applications. Furthermore, there exists a very close relationship between these two special classes of filters in such a way that a half-band filter can be derived from a Hilbert transformer in a straightforward manner and vice versa. It has been shown that these two classes of filters may be synthesized using the frequency-response masking (FRM) technique resulting in very efficient implementation when the filters are very sharp. While filters synthesized using the FRM technique has been characterized for the general low-pass case, Hilbert transformers and half-band filters synthesized using the FRM technique have not been characterized. The characterization of the two classes of filter is a focus of this paper. In this paper, we re-develop the FRM structure for the synthesis of Hilbert transformer from a new perspective. This new approach uses a frequency response correction term produced by masking the frequency response of a sparse coefficient filter, whose frequency response is periodic, to sharpen the bandedge of a low-order Hilbert transformer. Optimum masking levels and coefficient sparseness for the Hilbert transformers are derived; corresponding quantities for the half-band filters are obtained via the close relationship between these two classes of filters.Index Terms-Finite-impulse response (FIR) digital filter, frequency-response masking (FRM), Hilbert transformer, half-band filter, sparse coefficient filter.

Characterization of Non-Stationary Signals in Electric Grids: A Functional Dictionary Approach

“…where ω lb is the lower pass-band frequency and δ is the pass-band ripple. However, analysis of power grid waveforms operating near nominal frequencies (e.g., 50 or 60 Hz) would require an FIR Hilbert filter with a very high filter length L H and a prohibitive number of coefficients in order to achieve the necessary transition width ω lb and low ripple [39]. Fortunately, several alternatives to the Parks-McClellan technique exist to build efficient and sharp Hilbert filters.…”