I am fairly new DSP, and am using maths that I have not used in 20-30 years. I have been working with Cookbook formulae for audio EQ biquad filter coefficients by Robert Bristow-Johnson and am having a few problems.
I am trying to design a biquad band pass filter with a sampling rate of 48000 Hz, a center frequency of 20000 Hz, and a bandwidth of 500Hz. Q = fc/delta f, so Q should = 20000/500 = 40. I have run these numbers through a few different tools that use the Robert Bristow-Johnson formulas, and calculated them manually, and get the following coefficients:
a1 = 1.72129273 a2 = 0.98757764 b0 = 0.00621118 b1 = 0.00000000e+0 b2 = -0.00621118
I have plotted the frequency response with various tools (https://arachnoid.com/BiQuadDesigner/, source from http://www.earlevel.com/main/2016/12/01/evaluating-filter-frequency-response/ and others). I expected to see a -3db roll off at about 19750Hz/20250Hz, but I see it at about 19950Hz/20050Hz. Could anyone point out what I am doing wrong.