1st-order filter implementation question

dimitris. Question

Mar 16, 2015 00:00

Hi forum,

I was wondering if there is anything wrong with the definition of the first-order filter in the help of SigmaStudio.

I found the following definition for the first-order filter:

However when I am trying a high pass filter with a cut-off frequency at 1000 Hz then get the coefficients that appear below:

Now, if the definition of the implementation is right, then for a gainLinear operator of 1 (meaning gain 0), for a highpass filter, I should get a1=b0=-b1.

But clearly this is not the case as the 3 coefficients that are being produced in SigmaStudio are not all the same.

Could you please enlighten me on if I am missing something?

thank you

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jobo23 Reply

Mar 16, 2015 00:00

Moving to the SigmaStudio forum for discussion.

-Joe

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KJBob Reply

Mar 16, 2015 00:00

Hello dimitris,

The formulas above are OK for lowpass, but Steven W. Smith's DSP book shows different ones for hi-pass (it also swaps the "a" and "b" coefficients compared to SigmaStudio's convention, besides flipping the sign of the "a" coefficient). Here's how to calculate the coefficients (these formulas cover only the case of gainlinear = unity):

fo (cutoff freq) = 1000 Hz

fs (sample rate) = 48000 Hz

First calculate w = 2*pi*fo/fs = 0.1308997

Then, calculate x = e^(-w) = e^ (-0.1308997) = 0.8773

Finally figure the coefficients: b0 = (1 + x) / 2 = 0.98365

b1 = - bo = -0.98365

a1 = x = 0.8773

One of the General Second-Order filters allows you to type in coefficients as shown above -- this is handy when troubleshooting coefficients.

Best regards,

Bob