Z Transform Calculator and Table

Z Transform Calculator


Solve for:


Oh snap!

An error occurred while processing this operation.

The Z Transform Calculator is one of the few online tools that allows you to calculate the z-transform of a function. To calculate z-transforms with this calculator you only have to perform three simple steps:

  1. Choose the independent variable that you will use as a reference to compute the z-transform.
  2. Enter the mathematical expression you want to transform to the z-domain. To do this you must use the allowed functions that are presented in table number 1.
  3. Press the “Solve” button and doing so will display a box with the solution.


Valid functions and symbols Description
sqrt() Square root
ln() Natural logarithm
log() Logarithm base 10
^ Exponents
abs() Absolute value
sin(), cos(), tan(), csc(), sec(), cot() Basic trigonometric functions
asin(), acos(), atan(), acsc(), asec(), acot() Inverse trigonometric functions
sinh(), cosh(), tanh(), csch(), sech(), coth() Hyperbolic functions
asinh(), acosh(), atanh(), acsch(), asech(), acoth() Inverse hyperbolic functions
pi PI number (π = 3.14159...)
e Neper number (e= 2.71828...)
i To indicate the imaginary component of a complex number.
u() Heaviside step function
Table 01: Valid functions and symbols


What is Z-Transform?

The Z-Transform is a tool that provides a method to characterize signals and discrete-time systems by means of poles and zeros in the Z domain.

The Z Transform, X(z), is the equivalent of the Laplace Transform for discrete time. Since z is a complex variable, the domain Z is a complex plane.

The Z-transform X(z) of a signal x[n] is defined as the power series:

X(z) = +∞x = −∞ x[nzn
Z Transform formula

where z is a complex variable and the sum is taken over all possible values of n.

The Z-transform is a mathematical tool used to analyze discrete-time signals and systems. It is a powerful tool for understanding the behavior of such systems, and it has numerous applications in engineering, including in the fields of electrical engineering, control engineering, and digital signal processing.

The Z-transform has a number of useful properties, including linearity, time shifting, and frequency shifting. It can also be used to find the transfer function of a discrete-time system, which describes how the system responds to different input signals.

One of the key benefits of the Z-transform is that it allows us to analyze the behavior of discrete-time systems in the frequency domain, using techniques that are similar to those used to analyze continuous-time systems in the frequency domain using the Laplace transform. This makes it possible to understand the frequency response of discrete-time systems and to design filters and other types of signal processing systems.

Overall, the Z-transform is a powerful and versatile tool for understanding and analyzing discrete-time systems, and it has numerous applications in engineering and other fields.

Z-transform properties table

z transform properties

Z Transform Table

Made with