Z-transform is a mathematical tool, which transforms the time-domain mathematical model and difference equation of discrete system into simpler frequency-domain mathematical model and algebraic equation to simplify the solution process. Z is a complex variable with a real part and an imaginary part. It is usually expressed in polar coordinates. The plane formed by taking the real part of Z as abscissa and the imaginary part as ordinate is called Z plane, which is the complex domain plane of discrete system.

Z-transform can transform time-domain signals (that is, discrete time series) into complex frequency-domain expressions. Its position in discrete-time signal processing is the same as that of Laplace transform in continuous-time signal processing.