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" <

[hidden email]>

To: <

[hidden email]>

Sent: Saturday, December 15, 2012 9:15 AM

Subject: Re: [SoX-users] SoX plot coefficients

----- Original Message -----

> From: Ulrich Klauer <

[hidden email]>

> To:

[hidden email]
> Cc:

> Sent: Saturday, December 15, 2012 3:29 AM

> Subject: Re: [SoX-users] SoX plot coefficients

>

> Marco Bandiera <

[hidden email]>:

>

>> 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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