chebyshev.html

chebyshev.mws

syntfil[Chebyshev] - compute the Chebyshev approximation

Calling sequence:

Chebyshev(order, Os, ap, var)

Parameters:

order - order of the Chebyshev approximation [-]

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

ap - passband ripple [dB]

var - variable symbol in tranfer and characteristic function

Parameter order must be positive integer. Parameter ap must be positive number. Parameter var must be symbol . Parameter Os is not utilized and its type is not checked.

Description:

This function returns inverse transfer function and characteristic function .
Inverse transfer function is polynomial in variable var with degree order .
Characteristic function has form , where and

Info level:

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

infolevel[syntfil] =

2 - print polynomials of inverse transfer function and characteristic function on separate lines with description.

3 - as level 2 + print transfer function's poles and parameter .

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

Example:

> with(syntfil):

> infolevel[syntfil]:=3;

> Chebyshev(4,2,3,s);

epsilon = .9976283451

Poles of H:

[-.8517039862e-1+.9464844330*j, -.8517039862e-1-.9464844330*j, -.2056195314+.3920466889*j, -.2056195314-.3920466889*j]

Chebyshev:

G = 1.412537545+7.981026761*s^4+4.641604426*s^3+9.330758585*s^2+3.230463838*s

Phi = .9976283450+7.981026761*s^4+7.981026761*s^2

> infolevel[syntfil]:=1;

> G,Phi:=Chebyshev(4,2,3,s);

Magnitude frequency response

> plot(MagnitudeHdB(1/G)(omega),omega=0..3);

DroppNLP, TestCharEqn, MagnitudeH, MagnitudeHdB, PhaseH, GroupDelayH
in addition to Chebyshev approximation the following approximations can be used
Butterworth, InvChebyschev, InvChebyshevB, Cauer, CauerB, CauerC