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z-Transform Tutorial: z-Transform and Inverse z-Transform Examples & Functions

In analog or continuous systems the Fourier transform played a key role in analyzing signals and systems. The inverse z transform represents a time-domain sequence of a z transform function. We note that the z transform for digital signals or discrete-time signals is the digital counterpart of the Laplace transform for continuous-time signals. Both the [...] . . . → Read More: z-Transform Tutorial: z-Transform and Inverse z-Transform Examples & Functions

Overview and Introduction to the z-Transform (Polynomial & Rational Functions)

We introduce the z-transform bringing polynomials and rational functions to help analyze linear discrete-time systems. The discrete-time convolution (or FIR convolution) is equivalent to polynomial multiplication and algebraic operations in the z transform domain can be translated as combining or decomposing linear time-invariant (LTI) systems. The most common z-transforms are rational functions, that is, the [...] . . . → Read More: Overview and Introduction to the z-Transform (Polynomial & Rational Functions)

Convolution Sum for Discrete-Time Systems

Below is an introduction to the convolution sum for discrete-time systems. Once you characterize the system with a given impulse as an input and find it corresponding impulsive output, then any arbitrary input can be decompose as a summation of time-shifted weighted impulses. The resulting output is simply a summation of time-shifted weighted impulse responses. [...] . . . → Read More: Convolution Sum for Discrete-Time Systems