Hello,
I'm trying to calculate coefficients for a 4rth order Butterworth filter,
to be implemented as two cascaded biquads. It seems easy enough to come up with
the poles in the s domain and split the transfer function into two pairs of
complex conjugate poles, so that I have two 2nd-order sections that I can BLT
into biquads.
Say I want the complete fourth order filter, which I will obtain by cascading
two biquad sections, to have a cutoff of pi/16. Now, the two biquads will not
necessarily each have this same cutoff frequency themselves, right? I know I
can't simply cascade two biquads with the same coefficients because then I
get Linkwitz-Riley and I don't want that.
So, how do I apply the BLT to my two s-domain filters when I don't know the
cutoff frequencies of the individual filters that will sum to get what I
want?
Thanks in advance for any help!
4rth order digital Butterworth filter coefficient calculation
Started by ●April 7, 2009
Reply by ●April 8, 20092009-04-08
Ethan,
Yes, each section will have different pole locations and slightly different -3dB frequencies, but you don't need to be concerned about each section's -3dB frequency. You just need to know all four pole locations, then just apply the BLT where s = 2 * Fs * (z-1)/(z+1) and the two cascaded sections will combine to give your Butterworth response.
Gene Goff
1. 4rth order digital Butterworth filter coefficient calculation
Posted by: "e...@peavey.com" e...@peavey.com
Date: Tue Apr 7, 2009 3:41 pm ((PDT))
Hello,
I'm trying to calculate coefficients for a 4rth order Butterworth filter, to be implemented as two cascaded biquads. It seems easy enough to come up with the poles in the s domain and split the transfer function into two pairs of complex conjugate poles, so that I have two 2nd-order sections that I can BLT into biquads.
Say I want the complete fourth order filter, which I will obtain by cascading two biquad sections, to have a cutoff of pi/16. Now, the two biquads will not necessarily each have this same cutoff frequency themselves, right? I know I can't simply cascade two biquads with the same coefficients because then I get Linkwitz-Riley and I don't want that.
So, how do I apply the BLT to my two s-domain filters when I don't know the cutoff frequencies of the individual filters that will sum to get what I want?
Thanks in advance for any help!
Yes, each section will have different pole locations and slightly different -3dB frequencies, but you don't need to be concerned about each section's -3dB frequency. You just need to know all four pole locations, then just apply the BLT where s = 2 * Fs * (z-1)/(z+1) and the two cascaded sections will combine to give your Butterworth response.
Gene Goff
1. 4rth order digital Butterworth filter coefficient calculation
Posted by: "e...@peavey.com" e...@peavey.com
Date: Tue Apr 7, 2009 3:41 pm ((PDT))
Hello,
I'm trying to calculate coefficients for a 4rth order Butterworth filter, to be implemented as two cascaded biquads. It seems easy enough to come up with the poles in the s domain and split the transfer function into two pairs of complex conjugate poles, so that I have two 2nd-order sections that I can BLT into biquads.
Say I want the complete fourth order filter, which I will obtain by cascading two biquad sections, to have a cutoff of pi/16. Now, the two biquads will not necessarily each have this same cutoff frequency themselves, right? I know I can't simply cascade two biquads with the same coefficients because then I get Linkwitz-Riley and I don't want that.
So, how do I apply the BLT to my two s-domain filters when I don't know the cutoff frequencies of the individual filters that will sum to get what I want?
Thanks in advance for any help!
