Design of FIR Hilbert transformers and differentiators in the complex domain

Abstract

This paper presents a method for the design of FIR Hilbert transformers and differentiators in the complex domain. The method can be used to obtain conjugate-symmetric designs with smaller group delay compared to linear-phase designs. Non-conjugate symmetric Hilbert transformers are also designed. This paper is an extension of our previous work [1], which presented the algorithm for the design of standard frequency selective filters. The minimax criterion is used and the Chebychev approximation is posed as a linear optimization problem. The primal problem is converted to its dual and is solved using an efficient quadratically convergent algorithm developed by Tang [2]. When a constant group delay is specified, the filter designs have almost linear phase in the passbands. When the specified group delay is half the filter length, the algorithm results in exactly linear-phase designs.

Evaluation of Quadrature Signal Generation Methods with Reduced Computational Resources for Grid Synchronization of Single-Phase Power Converters through Phase-Locked Loops

“…Because its frequency response stretches across the entire spectrum, digital realization requires an approximation. Three main approaches can be found in the literature [48,49]: complex filters, which require complex and computationally expensive hardware multipliers; the combination of two filters that form 90 • , which are commonly implemented as delayed band-pass infinite impulse response (IIR) filters variables, which deteriorate PLL performance; and finite impulse response (FIR) filters, which require the real part to be delayed to adjust the relative phases of in-phase and quadrature signals. The latter approach is the preferred method for PLLs in grid-connected converters [40,41,50].…”

“…The latter approach is the preferred method for PLLs in grid-connected converters [40,41,50]. The type III and IV FIR filters can be applied as for the generation of the quadrature signal [51], but the necessary multiplications in type III are half those in type IV [49].…”

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

“…However, it should be noted that can be any low-order Hilbert transformer implemented using any structure such as those in [25]- [27] and can be designed independent on and . The frequency responses of and are than optimized as a correction term to sharpen the frequency response of the overall filter.…”

Real-Time Digital Timing in Positron Emission Tomography

“…In this case, the sample with the steepest slope in the vicinity of the rise edge is considered for the computation of the line that passes through and and the zero crossing of the interpolated line with the base level computed as shown in (6). (6) The previous expression can also be reformulated as a pulse filter plus interpolation to compute the crossing point with the base line, as shown in (7), taking into account that is a discrete differentiator [14].…”