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

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...

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Published inIEEE transactions on circuits and systems. I, Regular papers Vol. 60; no. 1; pp. 136 - 149
Main Authors Johansson, H., Hermanowicz, E.
Format Journal Article
LanguageEnglish
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
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Abstract 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.
AbstractList 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 dont-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.
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.
Author Johansson, H.
Hermanowicz, E.
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Snippet This paper considers two-rate based structures for variable fractional-delay (VFD) finite-length impulse response (FIR) filters. They are single-rate...
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SubjectTerms 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
Title Two-Rate Based Low-Complexity Variable Fractional-Delay FIR Filter Structures
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