Two-Rate Based Low-Complexity Variable Fractional-Delay FIR Filter Structures

• Published in: IEEE transactions on circuits and systems. I, Regular papers Vol. 60; no. 1; pp. 136 - 149
• Main Authors: Johansson, H., Hermanowicz, E.
• Format: Journal Article
• Language: English
• Published: IEEE 01.01.2013
• Subjects: Approximation error; Bandwidth; Complexity theory; Delay; Finite impulse response filter; FIR filters; frequency-response masking; half-band filters; linear phase; low complexity; low delay; minimax design; Periodic structures; TECHNOLOGY; TEKNIKVETENSKAP; Transfer functions; variable fractional delay
• ISSN: 1549-8328; 1558-0806
• DOI: 10.1109/TCSI.2012.2215697

This paper considers two-rate based structures for variable fractional-delay (VFD) finite-length impulse response (FIR) filters. They are single-rate structures but derived through a two-rate approach. The basic structure considered hitherto utilizes a regular half-band (HB) linear-phase filter and the Farrow structure with linear-phase subfilters. Especially for wide-band specifications, this structure is computationally efficient because most of the overall arithmetic complexity is due to the HB filter which is common to all Farrow-structure subfilters. This paper extends and generalizes existing results. Firstly, frequency-response masking (FRM) HB filters are utilized which offer further complexity reductions. Secondly, both linear-phase and low-delay subfilters are treated and combined which offers trade-offs between the complexity, delay, and magnitude response overshoot which is typical for low-delay filters. Thirdly, the HB filter is replaced by a general filter which enables additional frequency-response constraints in the upper frequency band which normally is treated as a don't-care band. Wide-band design examples (90, 95, and 98% of the Nyquist band) reveal arithmetic complexity savings between some 20 and 85% compared with other structures, including infinite-length impulse response structures. Hence, the VFD filter structures proposed in this paper exhibit the lowest arithmetic complexity among all hitherto published VFD filter structures.