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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.

Parents
  •      Hello Hushan,

         You could say that both are correct -- they're just different representations of the same thing.  DSP literature, I'm afraid, is subject to this sort of confusion.  For example, the reference I cited above, from Steven W. Smith's book Digital Signal Processing -- A Practical Guide for Engineers and Scientists, refers to feedforward coefficients with the letter a, and feedback coefficients with the letter b.  In other literature as well as in SigmaStudio, the a's and b's are flopped.

         The a coefficients' reversed polarity you discovered originate from the mathematical expression of the filter's transfer function.  In there, all the feedback coefficients show with minus signs.  Some DSP authors leave the minus signs in the formula, others transfer them to the coefficients.  In SigmaStudio, the a coefficients the program generate (or those you type into the boxes) are the polarity the math produces -- afterward they're negated when sent to the DSP (what you see in the Capture window).  Perhaps flipping their signs in SigmaStudio minimizes instruction usage in the DSP.

         Thus, if you have a microcontroller safeloading coefficients directly to the DSP, you need to flip the signs of the a coefficients yourself.  This particular confusion is so bad that more than one DSP reference suggests that you might as well toss a coin when giving signs to the feedback coefficients -- and if they don't work, just try the other way.

         Best regards,

         Bob

Reply
  •      Hello Hushan,

         You could say that both are correct -- they're just different representations of the same thing.  DSP literature, I'm afraid, is subject to this sort of confusion.  For example, the reference I cited above, from Steven W. Smith's book Digital Signal Processing -- A Practical Guide for Engineers and Scientists, refers to feedforward coefficients with the letter a, and feedback coefficients with the letter b.  In other literature as well as in SigmaStudio, the a's and b's are flopped.

         The a coefficients' reversed polarity you discovered originate from the mathematical expression of the filter's transfer function.  In there, all the feedback coefficients show with minus signs.  Some DSP authors leave the minus signs in the formula, others transfer them to the coefficients.  In SigmaStudio, the a coefficients the program generate (or those you type into the boxes) are the polarity the math produces -- afterward they're negated when sent to the DSP (what you see in the Capture window).  Perhaps flipping their signs in SigmaStudio minimizes instruction usage in the DSP.

         Thus, if you have a microcontroller safeloading coefficients directly to the DSP, you need to flip the signs of the a coefficients yourself.  This particular confusion is so bad that more than one DSP reference suggests that you might as well toss a coin when giving signs to the feedback coefficients -- and if they don't work, just try the other way.

         Best regards,

         Bob

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