Fractional order elliptic filter design method of amplitude non-attenuation equilibrium phase

A filter design, non-attenuation technology, applied in the direction of digital technology network, impedance network, electrical components, etc., can solve the problems of large output delay and poor phase characteristics of elliptic filters, achieve flexible order adjustment and improve linearity , the effect of compensating phase delay

A filter design, non-attenuation technology, applied in the direction of digital technology network, impedance network, electrical components, etc., can solve the problems of large output delay and poor phase characteristics of elliptic filters, achieve flexible order adjustment and improve linearity , the effect of compensating phase delay

CN112332809AActive Publication Date: 2021-02-05HUAQIAO UNIVERSITY
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  • Fractional order elliptic filter design method of amplitude non-attenuation equilibrium phase
  • Fractional order elliptic filter design method of amplitude non-attenuation equilibrium phase
  • Fractional order elliptic filter design method of amplitude non-attenuation equilibrium phase

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Embodiment Construction

[0026] The invention proposes a design method of the amplitude non-attenuating fractional order elliptic filter, so that the order of the elliptic filter can be changed from only an integer to any positive real number. Therefore, the order adjustment of the filter becomes more flexible. At the same time, due to the introduction of the inverse filter, the phase delay of the filter is effectively compensated, and the linearity of the elliptic filter is improved.

[0027] The square of the transfer function modulus of the L(L>0) order fractional elliptic low-pass filter is:

[0028]

[0029] Among them, R L (Ω) is the improved Jacobian function, ε is the ripple coefficient of the elliptic filter.

[0030] It is known that the maximum passband ripple attenuation of the elliptic low-pass filter is Ω p dB, minimum stopband ripple attenuation in Ω a dB, select the coefficient k, then the design goal of the fractional elliptic filter is to design a i , b i and c i (i=1,2,...

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Abstract

The invention provides a fractional order elliptic filter design method of an amplitude non-attenuation equilibrium phase. The method specifically comprises the following steps: firstly, initializingan algorithm, designing an all-pass filter of which the amplitude is attenuated, converting the order of the elliptic filter into any positive real number from an integer, and then introducing an amplitude non-attenuation reverse filter to obtain an amplitude non-attenuation equilibrium phase; estimating that the error signal amplitude is not attenuated and the phase is a negative phase, and effectively compensating the phase of the fractional order analog filter. According to the fractional order elliptic filter design method of the amplitude non-attenuation equilibrium phase, the order adjustment of the filter becomes more flexible, due to the introduction of the reverse filter, the phase delay of the filter is effectively compensated, the linearity of the elliptic filter is improved; meanwhile, the amplitude of the filter is not attenuated, therefore, the steep transition zone characteristics of the elliptical filter are not changed, the comprehensive performance of the filter is improved, and the method has good engineering practicability.

Description

technical field [0001] The invention relates to the field of filter design, in particular to a fractional order elliptic filter design method with amplitude non-attenuation equalization phase. Background technique [0002] Elliptic filters are widely used in modern intelligent system design. Compared with other filters, such as Chebyshev type I and type II filters have stopband and passband smooth characteristics, and Butterworth filter passband and stopband have smooth characteristics at the same time, elliptic filters sacrifice passband The smooth line and linearity of the stop band and the stop band are expected to obtain the characteristics of a steep transition band. Theoretical research shows that, when the other performance conditions of the filter are the same, the elliptic filter has the best ripple in the passband and stopband, and the steepest transition band. The reason is that its filter transfer function has both zeros and poles. A large number of zero-pole ...

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Application Information

Patent Timeline
05 Feb 2021
Publication
CN112332809A
IPC
H03H17/02
CPC
H03H17/02; Y02D30/70
Inventors
傅文渊; 周静敏