Taps for simple IIR Filter in GNU Radio

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SUMMARY

This discussion focuses on implementing a 2nd order IIR filter at 170 Hz using GNU Radio's Companion graphical editor, with a sample rate of 16000 samples/sec. The user derived the filter taps using Mathematica, resulting in feedforward taps of [1] and feedback taps of [1.97559, -0.9801]. However, upon entering these values into GNU Radio, the output did not match expectations, leading to instability when toggling the tap polarity convention. The conversation highlights the importance of understanding the IIR block's implementation details and suggests reviewing the source code for clarity.

PREREQUISITES
  • Familiarity with GNU Radio Companion for audio processing
  • Understanding of IIR filter design principles
  • Basic knowledge of Mathematica for calculating filter coefficients
  • Experience with signal processing concepts, particularly impulse response
NEXT STEPS
  • Investigate the GNU Radio IIR block's source code for implementation details
  • Learn about the differences between "old" and "new" conventions for tap polarities in IIR filters
  • Explore additional examples of IIR filter implementations in GNU Radio
  • Study the effects of varying Q factors on filter stability and performance
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Audio engineers, signal processing enthusiasts, and developers working with GNU Radio who are interested in implementing and troubleshooting IIR filters.

Swamp Thing
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I am experimenting with GNU Radio (using the Companion graphical editor) to do some simple audio processing.

As my first experiment, I am trying to set up a very simple 2nd order IIR filter at 170 Hz with a sample rate of 16000 samples/sec. I used this Mathematica code to find the taps:
Code: 
fs=16000;
fr=170 (* Center Frequency *)
\[CapitalTheta]=N[2 Pi fr / fs ]

r=0.99; (* this controls the Q *)

t1=2 r Cos[\[CapitalTheta]]
t2= -r*r
{t1,t2} (* these are the tap values that I want to use in GNU Radio's IIR block *)

Here's how I verify within Mathematica that the filter should work OK:
Code: 
y1=0;
y2=0;
yyy=Reap[For[i=0,i<400,i++,
       x=If[i<4,10,0];  (* inputs a short pulse to the system *)
       y=x + t1* y1 + t2*y2;
      Sow[y];
        y2=y1;
        y1=y;

    ]
][[2,1]];
ListPlot[yyy,PlotRange->All]

And this gives this plot, where I can verify that the resonant frequency is around 170 Hz as intended.

1728912835643.png


Now when I enter the feedforward taps into the GNU Radio IIR as [1] and the feedback taps as [1.97559, -0.9801] --- which I got from the first code block above and which works in the test filter above --- I get nothing resembling the above.

The impulse response in GNU Radio looks like this:

iir.png


Now, the IIR block has a dropdown that selects the so-called "old" or "new" convention for the polarities of the tap values. If I change that option, I get the following, where the filter seems to have become unstable and is "hunting" at the sample rate.
iir-2.png


So if anyone knows about the quirks of the IIR block in GNU Radio, please help me understand this. Thanks.
 
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I don't use GNU Radio but I've done some IIRs using liquid-dsp. My suggestion is to look at the source code for the IIR block. Walk through what it's actually calculating for the inputs you've given it. The one nice thing about open source is you have the source.