Practical infinite impulse response (IIR) filters are usually based upon analogue equivalents (Butterworth, Chebyshev, etc.) using a transformation known as the bilinear transform which maps the $s$-plane poles and zeros of the analogue filter into the $z$-plane. However, it is quite possible to design an IIR filter without any reference to analogue designs, for example, by choosing appropriate locations for the poles and zeroes. Can somebody please explain the latter design of digital IIR filters (i.e., without any reference to analogue design) for the following simple example?
For a digital system with sampling frequency of 60 MHz, design a digital IIR filter with two complex conjugate poles at 23 MHz, and one zero at 18 MHz.
This is basically an equalizer for a lossy channel. The filter is flat at lower frequencies (DC attenuation), with a peaking at higher frequency and then drops rapidly. For that, only knowing the poles and zero locations should be enough which defines the DC attenuation, bandwidth, and boost (peaking) of the filter. The amount of boost or DC attenuation does not matter as they can be tweaked by changing the poles and zeros locations. So I don't think any further information is required here. But if so, simply make an assumption.