In mathematics and signal processing, the Z-transform converts a discrete-time signal, which is a sequence of real
It … See more

The foundational concept now recognized as the Z-transform, which is a cornerstone in the analysis and design of digital control systems, was not entirely novel when it emerged in the mid-20th century. Its embryonic … See more

The region of convergence (ROC) is the set of points in the complex plane for which the Z-transform summation converges (i.e. doesn't blow up in magnitude to infinity):
Let Expanding on the interval it becomes
Looking at t… See more

Parseval's theorem
Initial value theorem: If is causal, then
Final value theorem: If the poles of are inside the unit circle, then See more

Here:
is the unit (or Heaviside) step function and
is the discrete-time unit impulse function (cf Dirac delta function which is a continuous-time version). The two functions are chosen together s… See more