Design method of fractional order elliptic filter with linear phase

A filter design, ellipse filter technology, applied in the field of filters, can solve the problem of inability to accurately design the linear phase, and achieve the effect of flexible order adjustment, balanced phase disturbance and low frequency suppression

Active Publication Date: 2020-10-30
HUAQIAO UNIVERSITY
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  • Abstract
  • Description
  • Claims
  • Application Information

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Problems solved by technology

[0004] However, due to the presence of both zeros and poles in the elliptic filter, the linear phase cannot be precisely designed, so the study of the linear phase of the fractional filter circuit has stronger engineering practicability
So far, there is no relevant literature on the linear phase design method of fractional elliptic filters

Method used

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  • Design method of fractional order elliptic filter with linear phase
  • Design method of fractional order elliptic filter with linear phase
  • Design method of fractional order elliptic filter with linear phase

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Embodiment Construction

[0030] The present invention will be further described below through specific embodiments.

[0031] m(m∈R + ) order fractional elliptic low-pass filter transfer function modulus is

[0032]

[0033] in ε represents the ripple factor.

[0034] , l=0,1,2,...,k+1, set the initial number of iterations ξ=1, l represents the metering factor of the elliptic function;

[0035] Suppose the transfer function of the elliptic low-pass filter is

[0036]

[0037] where p r ,q r , (r=1,2,3,...,k) is the design parameter of the elliptic filter, and the cut-off frequency of the filter is ω c .

[0038] Simultaneously (1) and (2), and substituting s=jω, we get

[0039]

[0040] Simplifying (3), we can get

[0041]

[0042] The phase of the elliptic filter is

[0043]

[0044] The group delay of the elliptic filter is

[0045]

[0046] The Bessel filter has the best linear phase characteristics, but its transition band is relatively flat, resulting in poor amplitud...

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Abstract

The invention provides a design method of a fractional order elliptic filter with a linear phase. According to the method, a Bessel filter is cascaded behind a fractional order elliptic filter. The method specifically comprises the steps of: performing initialization, randomly generating an initial zero point and a pole of the fractional order elliptic filter; calculating a zero pole of the elliptic filter; performing algorithm iteration on a zero pole; outputting the optimal solution of the fractional order elliptic filter, respectively calculating the group delay of the elliptic filter and the group delay of the Bessel filter, carrying out the algorithm iteration, and finally outputting the order n of the Bessel filter and the optimal solution of the fractional order elliptic filter, thereby completing the design of the fractional order elliptic filter with the linear phase. According to the method, the nonlinear phase of the fractional order elliptic filter is compensated by utilizing the good phase characteristic of the Bessel filter, and the poor transition zone characteristic of the Bessel filter is compensated by virtue of the steep transition zone characteristic of the elliptic filter, so that the filter performance with excellent performance is obtained, and the method has good engineering practicability.

Description

technical field [0001] The invention relates to the filter field, in particular to a design method of a fractional-order elliptic filter with a linear phase. Background technique [0002] The elliptic filter is a filter based on the coexistence of zeros and poles, which can better approximate the characteristics of an ideal filter. Since this method is closely related to the elliptic function in determining the position of the poles and zeros, it is called an elliptic filter. The passband and stopband of the elliptic filter have equal ripple characteristics, and its transition band is steep. Compared with the traditional filter, under the same filtering performance requirements, the elliptic filter can use the smallest approximation order to obtain the optimal filtering performance. [0003] Due to the discovery of the fractional-order impedance phenomenon, the fractional-order characteristics of filter circuits cannot be ignored. Fractional-order control not only has a b...

Claims

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Application Information

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Patent Type & Authority Applications(China)
IPC IPC(8): H03H17/02
CPCH03H17/0252
Inventor 傅文渊
Owner HUAQIAO UNIVERSITY
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