Re: [SoX-users] SoX plot coefficients

[Marco B. <mar...@gm...>]

Thank you very much sirs and, please, excuse my poor english language.

Yes, I want to calculate a1, a2, b0, b1 and b2 from frequency, gain and 
slope (or bandwith).
Indeed, by opening with an editor the *.plt files resulting form SoX --plot 
gnuplot command, I find this formula for the amplitude response:

H(f)=sqrt((b0*b0+b1*b1+b2*b2+2.*(b0*b1+b1*b2)*cos(f*o)+2.*(b0*b2)*cos(2.*f*o))/(1.+a1*a1+a2*a2+2.*(a1+a1*a2)*cos(f*o)+2.*a2*cos(2.*f*o)))

I could use it to plot the amplitude response curve with a program unlike 
Gnuplot, if I had the formulas to calculate a1, a2, b0, b1 and b2.
Excuse me but, due to my lacking mathematical knowledge, I didn't find the 
formulas I need in the Bristow-Johnson's paper.

Regards.

Marco Bandiera


----- Original Message ----- 
From: "Sergei Steshenko" <ser...@ya...>
To: <sox...@li...>
Sent: Saturday, December 15, 2012 9:15 AM
Subject: Re: [SoX-users] SoX plot coefficients




----- Original Message -----
> From: Ulrich Klauer <ul...@ch...>
> To: sox...@li...
> Cc:
> Sent: Saturday, December 15, 2012 3:29 AM
> Subject: Re: [SoX-users] SoX plot coefficients
>
> Marco Bandiera <mar...@gm...>:
>
>>  Where could I find the formulas for coefficients a1, a2, b0, b1, b2?
>
> I'm not sure what you are looking for, but if you want to calculate a*/b*
> from the filter frequency and bandwidth etc., the description is here:
> http://www.musicdsp.org/files/Audio-EQ-Cookbook.txt
>
> Ulrich
>

SoX assums B(z)/A(z) (_not_ A(z)/B(z)) form:

"
biquad b0 b1 b2 a0 a1 a2
Apply a biquad IIR filter with the given coefficients. Where b* and a* are 
the numerator and denominator coefficients respectively.

See http://en.wikipedia.org/wiki/Digital_biquad_filter (where a0 = 1).

This effect supports the --plot global option.
".

Both B(z)/A(z) and A(z)/B(z) can be seen in different textbooks.

Regards,
Sergei.


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