arcblock.html

syntfil[ARCBlock] - distribution of gain to particular biquads of cascade active filter

Calling sequence:

ARCBlock(params);

ARCBlock(params, h0);

Parameters:

params - table of biquadratic transfer functions parameters and with filter type (output of NLP2LP , NLP2HP , NLP2BP , NLP2BP2 or NLP2BS functions)

h0 - (optional parameter) gain of ARC filter - number that determine general gain or list of numbers that determine gain of particular sections (biquads). General gain is set to 1 if parameter h0 is not specified.

Description:

The function returns table with same structure as input table, however the output table contains gain values of particular sections in addition.
General gain is distributed so that dynamic of whole filter is balanced. It means that all maxima of magnitudes after each section (block) in cascade filter structure have the same level. Limitation of signal then appears in all blocks at same level of excitation signal.
The general gain is first distributed for case h0=1, then particular biquad gains are multiplied by particular numbers of a list, if parameter h0 is entered in form of a list. Dynamic conditions of cascade filter structure are given by gain partition in the list.

Definition of cascade filter transfers

transfer function after block , tj. ,

where is transfer function of block (biquad) ,

whereas and is Laplace transform parameter.

Info level

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

infolevel[syntfil] =

2 - print of particular block gains

3 - print of maxima modulus frequencies of block transfer functions (only for blocks with modulus camber), print of maxima modulus frequencies of the transfer functions (shift of maxima modulus frequencies of the transfer functions ) + print of level 2

Examples:

> with(syntfil):

> Gc,poles:=ButterworthPoles(8,3,20):

> lp:=NLP2LP(1000,Gc,poles);

> ARCBlock(lp,4);

> infolevel[syntfil]:=3:

> h0:=[3,2,1,1]:

> ARCBlock(lp,h0);

ARCBlock:

Frequencies of modulus peaks of particular blocks: [[2, 464.18662], [3, 721.24110]].

Frequencies of modulus peaks after particular blocks: [[2, [0.]], [3, [0., 657.58607]], [4, [0., 0.]]].

ARCBlock:

Amplification of particular blocks h0 = [3.000000, 2.000000, 0.610386, 1.638308].

See also:

NLP2LP, NLP2HP, NLP2BP, NLP2BP2, NLP2BS

ARCBlock1, ARCSynt

ARCSyntLP, ARCSyntHP, ARCSyntBP, ARCSyntBS