The only 'authoritative' web reference (=very often linked) for calculating the coefficients for digital biquad filters seems to be this:


Does anywone knows if there is out there any othe good reference or tutorial explaining the role and usage of the parameters Q, BW, dbGain ?

For example: when shoud I use Q instead of BW in specifications ? And what exactly is the meaning of Q? For what I see it's related to the bandwidth of passband filters (in which unit? Hz or normalized frequency?), but maybe I'm wrong. If not, how are they related ?

When and how should I specify the dbGain param? If I build a bandpass filter with the above formulas, I get a gain higher than around f0. How to correctly scale the a,b coeffs to obtain a unitary gain ?

Here some other interesting info about Bandwidth (BW) and Q specifications


EDIT after answers

For what I see, one effect of the Q is to raise the selectivity on the center frequency, so a biquad bandpass with a higher Q should be more selective than a biquad with a lower one cutting down heavily the off-center frequency. BUT, in the example I have a singal with tho alternating sine wave with frequency 1000 and 3000 hz (FS is 44100):

Sines 1 and 3 kHZ

If i filter around the 3000 hz using a bandpass with a Q=2 I get a pretty good signal with little ripples in the bandstop (bandpass biquad coeff: b=[0.0939, 0, -0.0939], a=[1.0, -1.6492,0.8122])

Biquad Q = 2

So I decide to raise the Q up to 20 to lowering the ripples, but all I obtain is this ! (bandpass biquad coeff: b=[0.0103, 0, -0.0103], a=[1.0, -1.8014, 0.9795])

Biquad Q = 20

Why the Q=20 biquad bandpass seems to raise the frequency in the bandstop instead of cut it off and why it spreads even more the center frequency ? Why doesn't it make my signal sharper ? Is there a way to mitigate these issues ?

Thanks for the help !

  • $\begingroup$ Most of these questions can be answered quickly and easily with a simple Google search. E.g. "Q" or "Q factor" is a long-established way of defining filter "sharpness" which pre-dates DSP: en.wikipedia.org/wiki/Q_factor $\endgroup$
    – Paul R
    Oct 7, 2012 at 0:36

1 Answer 1


A biquad is simply a two-pole IIR filter, where both the numerator and denominator of the transfer function are quadratic equations. Thus, you can factor the coefficient equations, and then use any reference regarding a filter's behavior related to pole/zero placements in the Z-plane to determine the behavior.

One tutorial method I recall was a software package where you could drag the poles and zeros around and see a plot of the resulting response.

Q is a term from classic analog filter design which relates the inverse of bandwidth relative to center frequency. So, given a known center frequency, the use of Q or bandwidth (depending on your exact interpretation or measurement method) is roughly interchangeable (after reciprocating one of them).


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