Introduction to Z Transform Calculator:
Z transform calculator is an online tool used in digital signal processing (DSP) and engineering to calculate the Z-transform of a discrete-time signal or system. It is used to transform the function (real value or complex value) from the time domain to the frequency domain.
It is a beneficial tool for students, professionals, or researchers because this method is used to analyze discrete signal processing by simplifying the signal processing into the frequency domain in just one click.
What is Z Transform?
Z transform is a process that is used to convert a real-valued function into a complex value function in discrete mathematics. It is used to analyze the signal processing and control theory to change into a frequency domain.
It has different properties of Fourier transform like linearity, time-shifting, and convolution, which are useful in signal processing. You can use the inverse Z-transform to transform the given function back into the time domain.
Z transform Formula:
The Z transform formula is based on a sequence of real or complex-valued functions in a discrete-time domain.
$$ X(z) \;=\; \sum_{n= -\infty}^{\infty} x[n]z^{-n} $$
- x[n] is the sampling number of valued functions
- n is the indexing,n=1,2,3,4….
- z is the series of variable
- X(z) is the z transform
How to Find the Z-Transform?
To find the Z-transform problem, you can use our z transform calculator to automate the process or follow some simple steps that are given below in which you see how to convert a discrete-time signal into the frequency domain to the Z-domain. Here is a step-by-step guide to solving a Z-transform problem: Step-by-Step Guide for Solving Z-Transform Problems:
Step 1: Identify the discrete-time signal x[n] you need to transform and the initial condition that is given in the function.
Step 2: Apply the Z-transform formula X for finite-length sequences,
$$ X(z) \;=\; \sum_{n= -\infty}^{\infty} x[n]z^{-n} $$
Step 3: Substitute the signal x[n] into the Z-transform formula to evaluate the sum and simplify it.
Step 4: Identify the values of z for which the Z-transform converges for determining given system stability.
Step 5: You can use the algebraic or partial fraction decomposition method to simplify the Z-transform and get a solution.
Practical Example of Z-Transform Calculator:
A solved example of z transform is given below to let you understand how to solve such problems manually.
Example: Find the Z-transform of the following discrete-time signal, where u[n] is the unit step function.
$$ x[n] \;=\; a^n u[n] $$
Solution:
Given data is:
$$ x[n] \;=\; a^nu[n]\; and\; n \;=\; 0,1,2,... $$
Apply the formula of z transform,
$$ X(z) \;=\; \sum_{n=0}^{\infty} a^n z^{-n} $$
$$ X(z) \;=\; \sum_{n=0}^{\infty} (az^{-1})^n $$
The given real value function becomes the geometric series so,
$$ \sum_{n=0}^{\infty} r^n \;=\; \frac{1}{1-r}\; if\; |r| < 1: $$
The sum of infinite geometric series become,
$$ X(z) \;=\; \frac{1}{1 - az^{-1}} $$
Check the series of convergence which is,
$$ |az^{-1}|< 1 \rightarrow |z| > |a| $$
As you can see the geometric series is already converge,
$$ X(z) \;=\; \frac{1}{1-az^{-1}}, |z| > |a| $$
Therefore the z-transform of a given function is,
$$ x[n] \;=\; a^n u[n] \rightarrow X(z) \;=\; \frac{1}{1-az^{-1}}, |z| > |a| $$
How to Use the Z Transformation Calculator?
Z transformation of functions calculator has a simple design that helps you to solve the given z transform question instantly. Follow some steps to get results without any trouble. These steps are:
- Enter your function to find the z-transform solution in the input box.
- Review your given input function to get the exact solution of the z-transform question.
- Click on the Calculate button to get the result of the given z-transform function problems.
- If you want to check the working behind our z transform calculator then you can use the load example and get its solution.
- Click the “Recalculate” button for the calculation of more examples of z-transform functions with the solution.
Output From Z-Transform Calculator:
Z Transformation Calculator provides you with a solution as per your input problem when you click on the calculate button. It may include as:
- In the Result Box
Click on the result button so you get the solution to your z-transform question.
- Steps Box
When you click on the steps option, you get the result of Z Transform questions in a step-by-step process.
- Plot Step
When you click on this option it will give you the solution in the form of a graph as well for a visual understanding of the z transform function.
Benefits of Z Transformation of Functions Calculator:
Z Transform Calculator has multiple benefits that you get when you use it to solve z transform problems to get the solution immediately. Our tool only takes the input real or complex value function to provide a solution without doing any external effort. These benefits are:
- Z-Transform Calculator is a reliable tool as it always provides you with accurate solutions to given z-transform problems.
- It is an efficient tool that provides solutions to the given z-transform problems in a few seconds.
- Z Transformation Calculator is a learning tool that provides you with complete knowledge about the concept of z transform very easily through online platforms.
- It is a handy tool that solves z transform problems quickly without manual calculation.
- Z transformation of functions calculator is a free tool that allows you to use it for the calculation of real-valued functions without charging anything.
- It is an easy-to-use tool, anyone or even a beginner can easily use it for the solution of z-transform problems.
