Monotonic low-pass filters with improved stopband performance

Rakovich, B.D.; Lazovich, S.M.

doi:10.1109/tct.1972.1083420

Cited by 7 publications

(3 citation statements)

References 4 publications

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“…Starting with this, some other characteristic functions were produced such as the O-filters [8] where all the C-constants were taken to be equal, or the transitional Butterwort-Legendre filters exhibiting properties between the two originals [9][10][11] and [12]. In [9], the procedure of creating new transfer function was named 'generalization'.…”

Section: The Synthesis Criteriamentioning

confidence: 99%

Unified theory and state‐variable implementation of critical‐monotonic all‐pole filters

Topisirović

Litovski

Stošović

2013

Circuit Theory & Apps

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SUMMARYThe subject of synthesis of critical-monotonic low-pass amplitude characteristics will be revisited. Several new contributions will be given in order to: facilitate the choice of the proper transfer function, to allow cataloguing the transfer functions, to simplify the circuit synthesis procedure, and to perform synthesis in the form of a statevariable continuous time active filter. Four main criteria for transfer function synthesis will be implemented: maximally flat at the origin, maximum slope at the band-edge, maximal asymptotic attenuation, and minimal amplitude distortion in the pass-band. For every criterion, a class of filters will be generated and the coefficients of the transfer functions will be calculated and published for the first time (with one exception). Properties of the classes so generated will be quantitatively compared for the first time. The state-variable structure will be advised as the one with the simplest synthesis procedure. The procedure will be explained and the design process will be exemplified. Statistical tolerance analysis will be performed for the example solutions in order to complete the information for comparison.

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Section: The Synthesis Criteriamentioning

confidence: 99%

Unified theory and state‐variable implementation of critical‐monotonic all‐pole filters

Topisirović

Litovski

Stošović

2013

Circuit Theory & Apps

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“…where, with no loss of generality, we can substitute E' = 1. If the constraint of monotonic nondecreasing passband magnitude response is imposed, the characteristic function F,(w2) can be written in the form w Fn(w2)= lo x2q-'E,-q(x2)dx (2 ) with 4 = 1 and 4 = 2 for n odd and even, respectively. In order to obtain a nondecreasing passband response all zeros of the derivative function En-q(x2) in the passband must be of even multiplicity.…”

Section: Characteristic Functionmentioning

confidence: 99%

Explicit expression for the characteristic function of generalized legendre filters

Rakovich

Popović

1978

Circuit Theory & Apps

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SUMMARYThe explicit formula for the characteristic function of all-pole lowpass filters with monotonic passband magnitude response is derived. It is shown that the characteristic function of Legendre, Halpern, LSM and other known classes of monotonic magnitude all-pole filters that are synthesized from the magnitude squared function, can be obtained by assigning different values to a variable parameter in the general expression obtained. The approximation method consists of using a weighted least-mean-square norm to minimize the area under the first derivative of the characteristic function.

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“…The main references [5][6][7][8][9][10][11] indicate that the development of Butterworth filters was dedicated to the filters of monotonic (in the pass-band) amplitude-frequency response with some improvements at the pass-band edge and in the stop-band. The Bessel polynomial filters did not have any noticeable development (the reasons for this are discussed at the end of this paper).…”

Section: Introductionmentioning

confidence: 99%

Stokes polynomial filters

Filanovsky

2012

2012 IEEE 55th International Midwest Symposium on Circuits and Systems (MWSCAS)

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The paper considers a new class of filters with transfer functions using the polynomials introduced by the British physicist Sir G.G. Stokes. The filters are transitional between Bessel and Butterworth ones. When one compares the step-responses of Bessel, Stokes, and Butterworth filters of the same order and the same -3dB bandwidth then the result is following. The Bessel filters have a certain delay and (practically) no overshoot in their step-transient response. The Stokes filters have larger delay than Bessel filters and a small overshoot. Finally, the Butterworth filters have largest delay and largest overshoot. The paper illustrates these properties and describes the data required for synthesis of the Stokes filters.

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Monotonic low-pass filters with improved stopband performance

Cited by 7 publications

References 4 publications

Unified theory and state‐variable implementation of critical‐monotonic all‐pole filters

Unified theory and state‐variable implementation of critical‐monotonic all‐pole filters

Explicit expression for the characteristic function of generalized legendre filters

Stokes polynomial filters

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