- A second-order IIR filter (
*y*[*n*] =*x*[*n*] -*a*_{1}*y*[*n*-1] -*a*_{2}*y*[*n*-2]) can be designed with a single peak in its frequency magnitude response using coefficients of the form:*f*_{c}is the center frequency of the resonance peak,*T*_{s}= 1 /*f*_{s}is the sample period, and 0 <*r*< 1.0. The closer*r*is to 1.0, the narrower the bandwidth of the resonance peak. - As a further refinement, we can design the resonance filter such that the resonance peak always has a gain of 1.0 by specifing numerator (or feedforward) coefficients as:
*y*[*n*] =*b*_{0}*x*[*n*] +*b*_{1}*x*[*n*-1] +*b*_{2}*x*[*n*-2] -*a*_{1}*y*[*n*-1] -*a*_{2}*y*[*n*-2]. - An example digital resonance filter magnitude response is shown in Fig. 5. The coefficients were determined as indicated above with a 5000 Hz center frequency.

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