On the design transitional Legendre–Butterworth filters

2015

Circuit Theory & Apps

SUMMARY A new type of filter approximation, which utilizes orthonormal Legendre polynomials, referred to as sum‐of‐squared Legendre polynomials, is presented in this paper. Power transmission coefficient and the group delay of the proposed filter are compared with those of the Butterworth, Legendre–Papoulis, and Halpern filters. In order to illustrate the design of the proposed filter function, sum‐of‐squared Legendre polynomials coefficients and normalized element values of the low‐pass LC (inductor‐capacitor) ladder network prototype are given, up to the 10th degree. For continuous‐time domain filtering, doubly terminated LC ladder network topologies have very low sensitivities to changes of component values. In order to determine the effect of variation of all reactive components on the filter attenuation characteristic, the new sensitivity function has been proposed. Copyright © 2015 John Wiley & Sons, Ltd.

“…57). Different types of the low-pass filters with monotonic amplitude-frequency response are described in papers [12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nearly monotonic passband low‐pass filter design by using sum‐of‐squared Legendre polynomials

Živaljević

Stamenković

2015

Circuit Theory & Apps

“…Accordingly, the corresponding discrete-time filter's magnitude function can be obtained from the magnitude response (1) by replacing x with sin (Ω/2) / sin (Ω c /2) for the sine filter and with tan(Ω/2)/ tan(Ω c /2) for the tan filter [7], [12], where Ω is discrete-time frequency, and Ω c discrete-time cutoff frequency. In the first case the so-called discrete-time sine filter or all-pole filter is obtained, whereas the second case gives the discrete-time tan filter or pole-zero filter [7], [12].…”

Section: Discrete-time Filtersmentioning

confidence: 99%

“…Chebyshev filter [1] exhibits higher selectivity than Butterworth filter but also has ripples and significant variations of group delay in the passband. On the contrary, Bessel filter exhibits maximally flat group delay but very low selectivity A particular class of the all-pole filters includes filters derived from the product of two orthogonal polynomial components such as products of Legendre polynomials [2], product of Chebyshev polynomials [3], transitional ButterworthChebyshev [4], [5], product of Chebyshev of the first kind and Chebyshev of the second kind [6], Butterworth-Legendre [7], etc. Filter synthesis using product of orthogonal Gegenbauer (ultraspherical) [8] polynomials is proposed in this paper.…”

Section: Introductionmentioning

confidence: 99%

Discrete-Time Filter Synthesis using Product of Gegenbauer Polynomials

Stamenković²,

Krstić³

2016

RADIOENGINEERING

“…There are approximations that have a very good magnitude characteristic in detriment of their group delay characteristic, as, e.g. Butterworth, Chebyshev, Legendre [1] and their derivatives by Ku and Drubin [2]. The converse case occurs with other approximations, as, e.g.…”

mentioning

confidence: 99%

Lowpass filters approximation based on modified Jacobi polynomials

Stamenković²,

Krstić³

2017

Electron. lett.

Self Cite

he orthogonal Jacobi polynomials are not suitable for use as the characteristic function in the continuous-and discrete-time filter design, because they are not fulfilling the basic condition: to be pure odd or pure even. A simple modification of Jacobi polynomials, is performed to obtain a new filter approximating function is proposed. Magnitude frequency responses of obtained filters exhibit more general behaviour compared with that of classical Gegenbauer (ultraspherical) filters, due to one additional parameter available in the Jacobi polynomials. This parameter can be used to obtain magnitude response with either smaller passband ripple values (nearly monotonic behaviour), smaller group delay variations or sharper cutoff slope. The proposed modified Jacobi polynomials are not orthogonal, however, many known orthogonal polynomials can be obtained as theirs special cases.