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About Sigmastudio IIR coefficients

I'm a new comer to use Sigmastudio ,I have some question about the general 2nd-Order Filters module coefficients,I know how to calculate the five coefficients when use as  2nd-Order Filters,But I don't know how to calculate the five coefficients use as two first order Filters when use  2nd-Order Filters module.Forgive my spelling mistakes and looking forward to your professional reply.

best wishes for you,thank you.

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•      Hello hushan,

Welcome to the forum, you'll find many interesting uses for SigmaDSP and SigmaStudio.

Your question is a good one!  I could not find any docs on the combined first-order filter pairs.  As it turns out, it's possible to combine two first-order filters into one second-order structure using some basic z-transform theory -- something I knew nothing about until yesterday.  Studying this reference:  http://www.analog.com/media/en/technical-documentation/dsp-book/dsp_book_Ch33.pdf

over several hours, I learned just enough to cough up coefficients for a combination lowpass and highpass filter.

Download the attached spreadsheet and scroll to its far right end, where you'll find the section shown below.  Enter your system sample rate and desired frequencies and gains for your filters.  The needed coefficients then appear.  You can click on each cell to see its formula, enabling you to code the calculations into a microcontroller if desired.  This spreadsheet was started years ago by the legendary BrettG, a former ADI support engineer.  I've been gradually expanding it to cover more kinds of filters.

To test this math I built the project shown below.  When manually entering the coefficients into a second-order filter, the resulting response (green) matches that of the stock single-order highpass / lowpass filters (red):

The same sort of math could work out coefficients for two lowpass filters, two highpass filters, two allpass filters, etc.  If the first-order filters are identical, you might as well go with an ordinary second-order filter with a low Q (about 0.5 ) instead.  In any event, I'm not presently in the mood to figure out any additional cases -- the algebra brings back awful memories from school.

Best regards,

Bob

1st-2nd-Order_IIR_Coefficient_Calculator.xls
•      Hello hushan,

Welcome to the forum, you'll find many interesting uses for SigmaDSP and SigmaStudio.

Your question is a good one!  I could not find any docs on the combined first-order filter pairs.  As it turns out, it's possible to combine two first-order filters into one second-order structure using some basic z-transform theory -- something I knew nothing about until yesterday.  Studying this reference:  http://www.analog.com/media/en/technical-documentation/dsp-book/dsp_book_Ch33.pdf

over several hours, I learned just enough to cough up coefficients for a combination lowpass and highpass filter.

Download the attached spreadsheet and scroll to its far right end, where you'll find the section shown below.  Enter your system sample rate and desired frequencies and gains for your filters.  The needed coefficients then appear.  You can click on each cell to see its formula, enabling you to code the calculations into a microcontroller if desired.  This spreadsheet was started years ago by the legendary BrettG, a former ADI support engineer.  I've been gradually expanding it to cover more kinds of filters.

To test this math I built the project shown below.  When manually entering the coefficients into a second-order filter, the resulting response (green) matches that of the stock single-order highpass / lowpass filters (red):

The same sort of math could work out coefficients for two lowpass filters, two highpass filters, two allpass filters, etc.  If the first-order filters are identical, you might as well go with an ordinary second-order filter with a low Q (about 0.5 ) instead.  In any event, I'm not presently in the mood to figure out any additional cases -- the algebra brings back awful memories from school.

Best regards,

Bob

1st-2nd-Order_IIR_Coefficient_Calculator.xls
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