Ztransformácia
Z-transformácia, also referred to as the Z-transform or discrete-time Z-transform, is a mathematical tool used to analyze discrete-time signals and linear time-invariant systems by mapping a sequence x[n] into a complex function X(z). It is especially helpful for solving difference equations and for designing digital filters.
Formally, the bilateral Z-transform is defined as X(z) = sum_{n=-∞}^{∞} x[n] z^{-n}, where z is a complex
The convergence of these series holds only in a region of the complex plane called the region
Inversion retrieves x[n] from X(z) using contour integration or partial fraction expansion, given a known ROC.
Applications span digital signal processing and control, including spectral analysis, filter design, and the solution of