Design and FPGA implementation of lattice wave fractional order digital differentiator

Sharma, Abhay; Rawat, Tarun Kumar

doi:10.1016/j.mejo.2019.04.013

Cited by 12 publications

(7 citation statements)

References 37 publications

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“…The transfer function of an LWDF with low‐pass characteristics is given by 2 11

H_{N} ((), z) = c ([], A_{1} ((), z) + A_{2} ((), z))

where c is a scale factor; A 1 ( z ) and A 2 ( z ) are real, stable APFs of orders P and Q , respectively.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Realization of A 1 ( z ) and A 2 ( z ) as a cascade of first‐ and second‐order WDFs of APF structures, with P and Q being odd and even integers, respectively, leads to the following expressions 11,12 :

A_{1} ((), z) = \frac{- γ_{0} + z^{- 1}}{1 - γ_{0} z^{- 1}} \prod_{k = 1}^{F} \frac{- γ_{2 k - 1} + γ_{2 k} ((), γ_{2 k - 1} - 1) z^{- 1} + z^{- 2}}{1 + γ_{2 k} ((), γ_{2 k - 1} - 1) z^{- 1} - γ_{2 k - 1} z^{- 2}}

A_{2} ((), z) = \prod_{k = F + 1}^{F + G} \frac{- γ_{2 k - 1} + γ_{2 k} ((), γ_{2 k - 1} - 1) z^{- 1} + z^{- 2}}{1 + γ_{2 k} ((), γ_{2 k - 1} - 1) z^{- 1} - γ_{2 k - 1} z^{- 2}}

where, γ i ( i = 0, 1, …, 2 F + 2 G ) represents the adaptor coefficients; F = ( P − 1)/2; and G = Q /2.…”

Section: Problem Formulationmentioning

confidence: 99%

“…Since, for low-pass filters, P = Q − 1 or P = Q+1, hence, N is odd. Realization of A 1 (z) and A 2 (z) as a cascade of first-and second-order WDFs of APF structures, with P and Q being odd and even integers, respectively, leads to the following expressions 11,12 :…”

Section: Problem Formulationmentioning

confidence: 99%

“…LWDFs provide a computationally efficient structure with a much lower number of multipliers needed to realize a particular filter order than the direct‐form structures. The suitability of LWDFs for VLSI implementations can be attributed to their highly modular structures 11 …”

Section: Introductionmentioning

confidence: 99%

“…The suitability of LWDFs for VLSI implementations can be attributed to their highly modular structures. 11 This letter presents the optimal design of DFOBFs using LWDF. The adaptor coefficients of the LWDF are optimally determined, and stable models are achieved by formulating the constraints based on the stability triangle.…”

Section: Introductionmentioning

confidence: 99%

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Optimal design of lattice wave digital fractional‐order Butterworth filter

Mahata

Kar

Mandal

2020

Circuit Theory & Apps

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SummaryThis letter presents the design of digital fractional‐order Butterworth filter (DFOBF) of order (n+α), where n is an integer, and α ∈ (0,1), from the perspective of optimal realization. The magnitude–frequency characteristic of the DFOBF is optimally modeled using the computationally efficient lattice wave digital filters (LWDFs). Design examples for the third‐ and fifth‐order LWDF‐DFOBFs with various values of n, α, and cut‐off frequencies are presented.

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“…The transfer function of an LWDF with low‐pass characteristics is given by 2 11