# butterworth digital filter

Discussion in 'Homework Help' started by vead, Jan 2, 2014.

Nov 24, 2011
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I want to know how we design digital filter what formula is used to design butterworth digital filter by Z transform method
I have question

Example-design 5th order butterworth digital low pass filter with cutoff frequency 10KHz

please anyone help me what formula is used to design butterworth digital filter by Z transform method

2. ### LvW Well-Known Member

Jun 13, 2013
826
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vead, it is not as simple as you might think. There is not only one single formula for designing such a filter.
I don`t believe that it will be possible to give you the necessary instructions in such a forum. Instead, try to find a suitable book that can help to teach you some basics.
A rather good recommendation is "The Scientist and Engineering Guide to Digital Signal Processing" by Steven W. Smith (available - free ? - from Anaog Devices).

Nov 24, 2011
712
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First thanks for reply I don't want that anybody explain whole process I have book Steven W. Smith I am just asking if we know the order of filter and cutoff frequency then Its sufficient to design filter or I need to more information

4. ### LvW Well-Known Member

Jun 13, 2013
826
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I am not very familiar with digital filteres - however, I can tell you that you have some alternatives. That means: You do not need "more information", but you have to select a certain topology.
At first - make the choice: FIR or IIR (non-recursive, recursive).
Then, it is your goal to find the various filter coefficients for one of the the flter topologies. During this selection process you again have different strategies to approximate the filter response (impuls invariance, windowing, z-transformation with different EULER substitutions).

In principle, it is similar to analog filter design:
You have to select between various filter topologies (passive, active - all with different alternatives). Filter design is one of the most challenging tasks in the field of electronics.

5. ### atferrari AAC Fanatic!

Jan 6, 2004
3,271
1,279
Are you sure you have read that book? The section on filters seems quite complete for the basics.

I propose you a simple exercise: imagine that somebody asks YOU your own question and try to see if you could answer it. No surprise that you would find the answer yourself. LOT of my questions-to-be never came to be posted thanks to that.

Just go to the book again.

Nov 24, 2011
712
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this subject irritating me I am trying to understand in practical way with basic concept but I don't understand why I am having problem

7. ### LvW Well-Known Member

Jun 13, 2013
826
114
Perhaps the attached document can help? In chapt. 2.6 you will find some basics on digital filters.

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8. ### t06afre AAC Fanatic!

May 11, 2009
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Nov 24, 2011
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thanks its grate help

10. ### Nguyen Si Phuoc New Member

Dec 15, 2014
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Hi all,
Base on your question, for me there is one general formula for design digital filter using z-transform is called "Frequency transformation filter using Pascal matrix equations". For more details you can find it on this link