Does anyone have any good references for deriving parameters of an IIR Low pass/High Pass filter directly in the digital domain using the magnitude squared at the corner frequency?
I have been able to derive the parameters of a first order Low/High pass filter with 3 dB attenuation at the corner frequency i.e. calculating K and alpha in:-
H(Z) = k(1+z^-1)/(1-alpha*z^-1)
My issue is that I distinctly remember deriving the parameters using a 6 dB attenuation at the corner frequency in a DSP course I have done previously but I have forgotten the trigonometric identiftes used to finish the derivation.
The general procedure is as follows:- 1) Let w = 0/pi to calculate the gain term k such that there is a 0dB gain at 0/pi 2) Calculate the magnitude squared at the corner frequency to obtain a value for alpha in terms of the corner frequency.
The problem may be that it should be a second order filter or I am recalling the method for a band pass/stop filter but I'm not sure and it appears this method is not used very often except in the case of band pass/stop filters for parametric EQ.
I hope the question is clear and I will try to improve the structure with the responses so it will be useful for others. Any help will be apreciated