nlp2bs.html

nlp2bs.mws

syntfil[NLP2BS] - frequency transformation of transfer function poles and zeros of NLP to a particular biquadratic transfer function parameters of band-rejection filter

Calling sequence:

NLP2BS(fp, f_p, Gc, poles);

NLP2BS(fp, f_p, Gc, poles, zeros);

Parameters:

fp - lower cutoff frequency [Hz]

f_p - upper cutoff frequency [Hz]

Gc - leading coefficient of denominator polynomial of transfer function H [-]

poles - 1D arrays of transfer function poles

zeros - 1D arrays of transfer function zeros (only for Cauer and Inverse Chebyshev transformations)

Parameters fp , f_p and Gc must be positive and fp < f_p .

Description:

The function returns a table with description of filter type, value of gain constant and parameters , , ( ) of particular passband biquadratic transfer functions - sections . Pole-zero pairing and section arranging are made so that dynamic balancing and noise properties of final filter were optimal. Section number determines sequence of the section in cascade. The filter type is . This specification is necessary for transfer function compilation and for following filter synthesis. Biquadratic transfer function with gain constant is denoted by:

for elliptic lowpass section ( )
for elliptic highpass section ( ) and by
for (elliptic) notch section ( ).

Info level:

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

infolevel[syntfil] =

2 - print of gain constant and parameters , , ( ) of particular biquadratic transfer functions in the order of Q-factor magnitudes

3 - print of filter type + print of level 2

Examples:

> with(syntfil):

> x:=BS2NLP(1000,1200,3000,4000,3,30):

> N:=ChebyshevNLPOrder(x);

> Gc,poles:=ChebyshevPoles(N);

> NLP2BS(1000,4000,Gc,poles);

> Gc2,poles2,zeros2:=InvChebyshevPolesZeros(N):

> infolevel[syntfil]:=3:

> NLP2BS(1000,4000,Gc2,poles2,zeros2);

type = cascade_BS

H0 = 1.947291

omega_0 = 12566.37062, Q = 0.94876, omega_n = 12566.37062

omega_0 =  7925.27924, Q = 1.29955, omega_n =  9229.99680

omega_0 = 19925.31313, Q = 1.29955, omega_n = 17108.74595

omega_0 =  6440.05130, Q = 3.78220, omega_n =  7716.45418

omega_0 = 24520.56091, Q = 3.78220, omega_n = 20464.53808

>

NLP2LP, NLP2HP, NLP2BP, NLP2BP2

MakeH, ARCSynt, ARCBlock, ARCBlock1