Hello Shashank,
I'm interested in this stuff too, but I'm no expert. I've tried to give
some pointers below. Hopefully someone else will correct me if I've made
an error:
On 17/11/2012 8:24 PM, Shashank Kumar (shanxS) wrote:
I am a self taught Linux fanatic who is trying to teach himself Sound
Processing.
I have basic idea of signal processing.
My aim is to develop an intuition by which I can design a 2nd order
IIR audio filter given a 3dB bandwidth and a center frequency.
I am not following any specific book/text.
You might find these resources helpful:
A. RBJ's EQ cookbook has equations for the filter you want:
http://www.musicdsp.org/files/Audio-EQ-Cookbook.txt
I believe that Robert derives the digital filter from the analog
butterworth transfer function. This is the method where you start with
an s-plane prototype and then apply the bilinear transform to get a
z-plane form. You pre-warp the important frequencies (cutoff, bandwidth)
in the s-plane so they end up in the right place in the z-plane after
warping.
I too have struggled with the mathematics behind the coefficient
calculations. For me it comes down to understanding the derivation of
the s-plane prototypes. I never studied laplace transform or much other
continuous-domain maths. I think that would help and I should look at
this again.
My impression is that the usual intuition develops out of the analog
methods of filter bandwidth calculation, thus you need to understand
these things:
- laplace transform
- mathematical foundations of the butterworth filter in the analog domain
- bilinear transform + pre-warping method to z-plane I mentioned above.
B. Robert also wrote a paper that surveys the different coefficient
calculation methods, you might find that helpful in understanding the
relation between coefficient computation methods. I haven't looked at it
for a while, probably it addresses some of the issues I mention above:
"The Equivalence of Various Methods of Computing
Biquad Coefficients for Audio Parametric Equalizers":
http://thesounddesign.com/MIO/EQ-Coefficients.pdf
C. Jon Dattoro's "Implementation of Recursive Digital Filters
for High-Fidelity Audio" examines implementation structures suitable for
digital audio. I think that will help you with your second question
about the implementation of the filter itself:
https://ccrma.stanford.edu/~dattorro/HiFi.pdf
+ Errata: https://ccrma.stanford.edu/~dattorro/CorrectionsHiFi.pdf
Hopefully someone can correct me if I'm leading you astray...
Ross.
I understand as to where should I keep my zeros and poles in Z plane
so as to boost/attenuate a particular frequency.
But I am having 2 problems:
1. I can't control the bandwidth
2. The output there is some kind of aliasing in output sound. My
results for a basic LPF is on my blog (with sound o/p and freq
analysis): http://trystwithdsp.wordpress.com/2012/11/07/basic-lpf/
I know my filter sucks and I am stuck.
Can someone please give me a pointer regarding how should I improve my filters ?
Thanks a ton.
shashank
skype: shanx.shashank
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