Introduction to Fourier Transform Calculator:
Fourier transform calculator with steps is an online tool that helps you to find functions that are present in the frequency domain by converting them into a time domain function. Our tool is used to find and analyze the nature of a function that is made of sinusoidal components in a frequency domain.
The fourier coefficients calculator is an amazing online source that gives a solution of complex functions into periodic functions. You do not do manual calculations to solve these complicated questions by hand just use our tool and get a solution in less than a minute.
What is the Fourier Transform?
Fourier transform is a complex analysis method where it analyzes the functions, specifically the periodic which is composed of a combination of sinusoidal components. It is used to decomposes a function of time into its constituent frequencies from the original function
This type of transformation is commonly used in signal processing, image process, physics, mathematics, and engineering because it gives insights into the nature of a function to transform it into a periodic function.
Fourier Transform Formula:
The formula of fourier transform is denoted with a frequency function f(ω) that converts it into a periodic function f(t). The fourier transform formula used by the Fourier transform calculator.
$$ F \{ f(t) \} (\omega) \;=\; \int_{-\infty}^{\infty} f(t)e^{-i\omega t} dt $$
Here e-iωt is the angular frequency of waves during oscillation.
Evaluation Process of Fourier Coefficients Calculator:
The fourier calculator gives you an easy way to evaluate the Fourier transform function and get a solution in just one click without much effort. You just need to put your function into even complicated or lengthy functions only and get a result.
Let's see the steps used in the calculation process of the Fourier transformation calculator. These steps are:
Step 1:
Identify the given function f(x) and its limits
Step 2:
Put the given function f(x) in to fourier transform formula such as,
Step 3:
Simplify the formula of fourier transform after adding the f(x) value if possible.
Step 4:
Take the integral with respect to t because we want to convert them into a time domain function. For integration, you can use different methods to get solutions.
Step 5:
After integration, apply the limits and simplify it.
Step 6:
After simplification, you get the solution of your Fourier transform function from the frequency domain to the time domain.
You can see the below example to get further clarity about the fourier transform online calculation process.
Pratical Example of Fourier Transform:
The practical example of Fourier transform function will express, how to transform a Fourier function that is present in the frequency domain into a time domain function. It also gives you a clue how the Fourier transform calculator with steps solves such complex problems.
Example: Find the Fourier Transform of:
$$ f(x) \;=\; \biggr[ \begin{matrix} e^{-ax}, & a ≥ 0 \\ 0, & x < 0 \\ \end{matrix}, a > 0 $$
Solution:
Convert the given function into a Fourier transform formula,
$$ \hat{f} (k) \;=\; \int_{-\infty}^{\infty} f(x) e^{ikx} dx $$
The function f(x) is e-as,
$$ =\; \int_0^{\infty} e^{ikx -ax} dx $$
Solve the integral and apply the limit then your function solution is,
$$ =\; \frac{1}{a - ik} $$
How to Use the Fourier Transform Calculator?
The fourier coefficients calculator has a simple layout that helps you to understand how to use it for evaluating the frequency function into the time domain function only by following some simple steps that are:
- Enter the Fourier transform function that you want to evaluate in the input field.
- Enter the Fourier transform variable in the input field.
- Add the variable in which you transform your function in the next input box.
- Review the given function before hitting the calculate button to start the evaluation process in the fourier calculator.
- Click the “Calculate” button to get the result of your given Fourier transform function problem.
- If you are trying our fourier transformation calculator for the first time then you can use the load example to learn more about this method.
- Click on the “Recalculate” button to get a new page for finding more example solutions of Fourier Transform problems.
Outcome from Fourier Calculator:
Fourier Transform Calculator with steps gives you the solution from a given frequency function when you add the input value to it. It provides you with solutions that is:
- Result Option:
When you click on the result option then it gives you a solution to the given problem.
- Possible Steps:
When you click on it, this option will provide you with a solution where all the calculations of the Fourier Transform process are mentioned in detail.
Useful Features of Fourier Transformation Calculator:
The fourier coefficients calculator provides you with multiple useful features that help you to evaluate the fourier transform online and give you a solution without any difficulty. These features are:
- The fourier calculator is a free-of-cost tool so you can use it for free to find fourier transform problem solutions without paying any fee.
- It is an adaptable tool that can manage various types of Fourier transform functions to get solutions for these functions into the time domain.
- Our Calculator helps you to get conceptual clarity for the Fourier transform working process when you use it for practice by solving more examples.
- It saves the time that you consume on the calculation in the calculator of complex and lengthy problems of Fourier transform.
- It is a reliable tool that provides you with accurate solutions whenever you use it to calculate the Fourier transform function without any calculation error.
- Fourier Transform Calculator with steps provides the solution without asking for signup which means you can use it anytime even if you are not signing up multiple times in a day.
