Fractional Delay Filters—Design and Applications

Seislet transform and seislet frame

“…The coefficients of filter B(Z t ) can be determined, for example, by fitting the filter frequency response at low frequencies to the response of the phase-shift operator. This leads to a version of Thiran's maximally-flat all-pass fractional-delay filters (Thiran, 1971;Välimäki and Laakso, 2001). In order to characterize several plane waves, we can cascade several filters of the form A-9 in a manner similar to that of equation A-7.…”

Low-Sensitivity Design of Allpass Based Fractional Delay Digital Filters

“…All general IIR and allpass-based VFD filters are having a common drawback, consisting of considerable transients appearing every time when the filter is tuned. Suppression of these transients is a difficult problem, several methods to solve it are discussed in (Valimaki & Laakso, 1998); (Valimaki & Laakso, 2001); (Makundi et al, 2002) and (Hachabiboĝlu et al, 2007), but publications on this topic are very few and a lot more remains to be done. The main aim of the present chapter is to investigate and compare the existing and to develop new methods of design, realization and tuning of allpass-based FDFs and to increase the accuracy throughout minimization of their sensitivities.…”

Principles of fractional delay filters

“…The literature on IIR FD filters mainly concentrates on allpass filters, with notable exceptions, e.g., [13]. The following five allpass filter design methods were discussed in our review articles [4], [5 The design of allpass FD filters typically requires an iterative design algorithm or solving a set of linear equations. The simplest allpass FD filter design is the Thiran allpass filter that has closed-form coefficient formulas (k = 0, 1, 2, ..., N) [14], [15]:…”

“…Both examples are typical applications of fractional delay (FD) filters, i.e., situations where uniform sampling is used and interpolation between samples is required [3], [4], [5] † . Fractional delay means, assuming uniform sampling, a delay that is a noninteger multiple of the sample interval.…”

“…Employing fractional † Due to space limitations, we cannot refer to all relevant publications here. Many more references can be found in [5].…”