How do you design IIR digital filters from analog prototypes?

IIR filter design starts with analog prototype (Butterworth, Chebyshev, Elliptic) then transforms to digital. Transformation methods: Bilinear transform - maps s-plane to z-plane nonlinearly, frequency warping requires pre-warping critical frequencies, most common method. Impulse invariance - samples analog impulse response, can cause aliasing, suitable for lowpass. Design steps: Determine digital specifications, pre-warp frequencies, design analog prototype, apply bilinear transform. Butterworth is maximally flat; Chebyshev has ripple but sharper cutoff; Elliptic has ripple in both bands with sharpest cutoff for given order.