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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:

- Choose the independent variable that you will use as a reference to compute the z-transform.
- 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.
- 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 |

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:

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.