The bilinear transform is a special case of a conformal mapping (namely, a Möbius transformation), often used to convert a transfer function formula_1 of a linear, time-invariant (LTI) filter in the continuous-time domain (often called an analog filter) to a transfer function formula_2 of a linear, shift-invariant filter in the discrete-time domain (often called a digital filter although there are analog filters constructed with switched capacitors that are discrete-time filters). It maps positions on the formula_3 axis, formula_4, in the s-plane to the unit circle, formula_5, in the z-plane. Other bilinear transforms can be used to warp the frequency response of any discrete-time linear system (for example to approximate the non-linear frequency resolution of the human auditory system) and are implementable in the discrete domain by replacing a system's unit delays formula_6 with first order all-pass filters.