Concept

Bilinear transform

Summary
The bilinear transform (also known as Tustin's method, after Arnold Tustin) is used in digital signal processing and discrete-time control theory to transform continuous-time system representations to discrete-time and vice versa. The bilinear transform is a special case of a conformal mapping (namely, a Möbius transformation), often used to convert a transfer function H_a(s) of a linear, time-invariant (LTI) filter in the continuous-time domain (often called an analog filter) to a transfer function H_d(z) 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 j \omega axis, \mathrm{Re}[s]=0 , in the s-plane to the unit circle, |z| = 1 , in the z-plane. Other bilinear transforms can be used to warp the frequency response of any discrete-time linea
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