Lowpass filters approximation based on modified Jacobi polynomials

Stojanović, Nikola; Stamenković, Negovan; Krstić, Ivan

doi:10.1049/el.2016.3025

Cited by 3 publications

(3 citation statements)

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“…The magnitude‐squared characteristic function of a continuous‐time lowpass filter with m pairs of finite transmission zeros in the stopband can be written as

A_{n} ()(, Ω^{2}) = \frac{\prod_{i = 1}^{m} {({normalΩ}^{2} - {normalΩ}_{0 i}^{2})}^{2}}{\prod_{i = 1}^{m} {({normalΩ}^{2} - {normalΩ}_{0 i}^{2})}^{2} + ε_{p}^{2} λ^{2} {[J_{n}^{(α, β)} (Ω)]}^{2}} \leq 1

where

λ = \prod_{i = 1}^{m} ()(, Ω_{0 i}^{2} - 1)

Ω_{0 i}

is i th zero position and

Ω_{0 i} > 1

, n > 2 m denotes the filter degree, and

ε_{p}

is a passband edge ripple factor. The polynomial

{scriptJ}_{n}^{false(α, β false)} false(normalΩ false) = \frac{1}{C_{n}^{false(α, β false)}} [P_{n}^{(α, β)} (Ω) + P_{n}^{(β, α)} (Ω)]

is a modified Jacobi polynomials [1], generated by using the parity relation for Jacobi orthogonal polynomials

P_{n}^{false(α, β false)} false(normalΩ

…”

Section: Approximationmentioning

confidence: 99%

“…Introduction: In the recently published paper [1], the authors have reported that the modified Jacobi polynomials can be used to construct a useful allpole lowpass filter functions. For the given lowpass filter degree, two parameters of the modified Jacobi polynomial can be used to a trade-off between passband magnitude response having ripples or being nearly monotonic, transition band width, or group delay deviation in the passband [2].…”

mentioning

confidence: 99%

“…is a modified Jacobi polynomials [1], generated by using the parity relation for Jacobi orthogonal polynomials P (a,b) n (V) with parameters a and b, while the constant C (a,b) n has to be chosen in such a way that J (a,b) n (1) = 1. The proposed characteristic function, used in (1), is given by…”

mentioning

confidence: 99%

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Lowpass filters with almost‐maximally flat passband and Chebyshev stopband attenuation

Stamenković¹,

Stojanović

Krstić³

2017

Electron. lett.

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class of the almost-maximally flat (AMF) lowpass filters with Chebyshev stopband attenuation, referred to as AMF filters, is discussed. Allpole lowpass filters' transfer functions are first derived by using parameters a and b of modified Jacobi polynomials J (ab) n (V) such that passband attenuation is minimised, and obtained transfer functions are then augmented by adding one or several pairs of jV-axis transmission zeros. The magnitude characteristics of proposed filters are compared with those of the Chebyshev II filters and are found to be superior, both in the passband and in the stopband.

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“…The magnitude‐squared characteristic function of a continuous‐time lowpass filter with m pairs of finite transmission zeros in the stopband can be written as