Biquad calculator v3

The latest version of the biquad calculator. It also takes on the functionality of the frequency response grapher:

Sample rate (Hz)
Fc (Hz)
Q
Gain (dB)
a coefficients (zeros)
b coefficients (poles)

bigger: Yes.

more filters: I probably won’t go deep into allpass filters, but people ask about calculating their coefficients from time to time, so here it is. And added first order filters for comparison.

phase plot: In earlier versions of the calculator, phase wasn’t important, we’re interested in an amplitude response and live with the phase response. But in adding the allpass filter type, phase is everything. It’s also good to know for other filter types, and for plotting arbitrary coefficients.

frequency response grapher: Edit or paste in coefficients and complete the edit with tab or a click outside the editing field to plot it. You can change the plot controls, but if you change a filter control then the calculator will resume as a biquad calculator.

For instance, clear the b coefficients, and place this sequence into the a coefficients: 1,0,0,0,0,1. Then click on the graph or anywhere outside the edit field to graph it. That’s the response of summing a signal with a copy of it delayed by five samples, a simple FIR filter—a comb filter.

Because the calculator can also plot the response of arbitrary coefficients, the biquad calculator now displays the normalized b0 coefficient (1.0)—which you can ignore in a typical biquad implementation.

The coefficients fields accept values separated by almost anything—commas, spaces, new lines, for instance. And they ignore letters and values followed by “=”. You can use “a0 = 0.971, a1 = 0.215…”, for instance. Even scientific notation is accepted (“1.03e4”,).

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4 Responses to Biquad calculator v3

  1. Josh says:

    Very cool. Thank you so much.

    It doesn’t seem like the gain slider changes anything.

    • Nigel Redmon says:

      It’s subtle, but notice that the Gain field is dimmed for all but the filters where gain makes sense—peak and shelf filters.

  2. Jayanth says:

    Hai,
    I liked your content. Thank you so much.

    I have one small doubt.
    We are doing audio Equalizer testing, where the default values we are using for the Equalizer are:
    FC_lowShelf – 250
    FC_highShelf – 1000
    Sample rate – 44100
    gain – 6
    Q factor – 0.707
    If I use the above values I am getting noise when I run my code.

    What if I set “Gain= 0”? what is the impact?

    And the values used for “Sample Rate”, “Qfactor”, and “Gain” are the default configurations?

    • Nigel Redmon says:

      I don’t understand the question. Are you using my biquad code, or other? For the shelves, Q is not used, so the setting doesn’t matter. Gain is the gain of the shelf. You should not get noise.

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