invchebyshevpoleszeros.html

invchebyshevpoleszeros.mws

syntfil[InvChebyshevPolesZeros] - compute the poles and zeros of the transfer function for the inverse Chebyshev approximation

syntfil[InvChebyshevBPolesZeros] - compute the poles and zeros of the transfer function for the inverse type B Chebyshev approximation

Calling sequence:

InvChebyshevPolesZeros(order, Os, ap)

InvChebyshevBPolesZeros(order, Os, ap)

Parameters:

order - order of the Chebyshev approximation [-]

Os - stopband frequency of normalized lowpass (NLP) [1/s]

ap - passband ripple [dB]

Parameter order must be positive integer and for type B in addition even. Parameters Os and ap must be positive numbers where Os > 1 .

Description:

This function returns the leading coefficient of denominator polynomial of transfer function and two 1D arrays of transfer function's poles and zeros.

Count of poles is given by order parameter. Count of zeros for even order is equal to order and for odd order is equal to order -1. In case of type B the count of zeros is equal to order -2.

Inverse Chebyshev approximation of type B is computed from standard inverse Chebyshev approximation (type A).

Info level:

Setting of variable infolevel[syntfil] can be used to get more detailed results.

infolevel[syntfil] =

2 - print leading coefficient of denominator polynomial of transfer function and two 1D arrays of transfer function's poles and zeros on separate lines with description

3 - as level 2 + print parameter .

4 - as level 3 + print ellipse parameter ( , ) on which lies poles of transfer function and secondary parameter .

5 - for type B - as level 4 + print transfer function's poles and zeros for type A,

Example:

> with(syntfil):

> InvChebyshevPolesZeros(4,2,3);

> infolevel[syntfil]:=3:

> InvChebyshevBPolesZeros(4,2,3);

epsilon = .9976283451

InvChebyshevBPolesZeros:

Gc = 4.439194219

Poles = [-.3546723780+.9514318954*I, -.3546723780-.9514318954*I, -.9925077857+.4534771731*I, -.9925077857-.4534771731*I]

Zeros = [2.334469420*I, -2.334469420*I]

See also:

ChebyshevNLPOrder

InvChebyshev, Chebyshev_asnew

NLP2LP, NLP2HP, NLP2BP, NLP2BP2, NLP2BS, BodePlot

in addition to inverse Chebyshev approximation the following approximations can be used
ButterworthPoles, ChebyshevPoles, CauerPolesZeros, CauerBPolesZeros, CauerCPolesZeros