IIR Filter Recommendations

Hello again,

Thanks RBJ for the further information relating to the Q of a filter.
Currently I am implementing some 2nd Order IIR Lowpass filters from the
Orfanidis DSP book. However, these filters dont have a 'Q' control, just a
cutoff frequency. Is it possible for every filter to have a 'Q' control
parameter? I would like to add a 'Q' control to my lowpass and highpass
IIR filters but not too sure the exact way to approach it?

My 2nd Order Lowpass transfer function is:

%
%               1 + 2z^-1 + z^-2
%   H(z) = b -----------------------
%             1 - 2az^-1 + a^2z^-2
%

Would it be possible to incorporate 'Q' into this design? I compute b and
a as follows:

% Sampling rate in Hz
Fs = 44100;

% Cutoff frequency in Hz
fCut = 500;

% Cutoff frequency in rads per sample
wc = 2*pi*fCut/44100;

% Apply bilinear transform to angular cutoff
omega = tan(wc/2);

% Compute filter parameter alpha
alpha = omega;

% Compute coefficients in terms of alpha
a = (1 - alpha) / (1 + alpha); 

b = alpha / (1 + alpha);

This is for the 3dB attenuation at the cutoff case. i.e alpha =
tan(wc/2);

Again, would it be possible to add some sort of resonance control to this
design, so that the filter peaks higher at the cutoff frequency?
Thanks very much for any advice.

Cheers,
David
		
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