nlp2bp.html

nlp2bp.mws

syntfil[NLP2BP] - frequency transformation of transfer function poles and zeros of NLP to a particular biquadratic transfer function parameters of bandpass filter

syntfil[NLP2BP2] - frequency transformation of transfer function poles and zeros of NLP to particular biquadratic transfer functions parameters of bandpass filter

Calling sequence:

NLP2BP(f_p, fp, Gc, poles);

NLP2BP(f_p, fp, Gc, poles, zeros);

NLP2BP2(fm, delta_fp, Gc, poles);

NLP2BP2(fm, delta_fp, Gc, poles, zeros);

Parameters:

f_p - lower cutoff frequency [Hz]

fp - upper cutoff frequency [Hz]

fm - passband geometric cetre [Hz]

delta_fp - passband width [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 f_p , fp , fm , delta_fp and Gc must be positive and f_p < fp .

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 nonelliptic section of bandpass filter (BP),
for elliptic lowpass section ( ) and by
for elliptic highpass 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:=BP2NLP(1000,1200,3000,4000,3,30):

> N:=ChebyshevNLPOrder(x);

> Gc,poles:=ChebyshevPoles(N);

> NLP2BP(1200,3000,Gc,poles);

> x:=BP22NLP(1900,1800,2600,3,30):

> N:=ChebyshevNLPOrder(x);

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

> infolevel[syntfil]:=3:

> NLP2BP2(1900,1800,Gc,poles2,zeros2);

type = cascade_BP

H0 = 0.214505

omega_0 = 11938.05209, Q = 0.76124

omega_0 =  7812.55049, Q = 1.35371, omega_n =  4423.70888

omega_0 = 18242.06933, Q = 1.35371, omega_n = 32216.65153

omega_0 =  7548.19679, Q = 4.99978, omega_n =  6117.94494

omega_0 = 18880.94488, Q = 4.99978, omega_n = 23294.92814

NLP2LP, NLP2HP, NLP2BS

MakeH, ARCSynt, ARCBlock, ARCBlock1