## Introduction to Fourier Transform Calculator:

Fourier transform calculator with steps is an online tool that helps you to **find functions** (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 up of sinusoidal components in a frequency domain.

The fourier coefficients calculator is an amazing online source that convert complex functions into periodic functions. You do not need to manually calculate the complicated questions, 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 decompose a function of time into its constituent frequencies from the original function.

This type of transformation is commonly used in signal processing, image processing, physics, mathematics, and engineering. 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 is:

$$ F \{ f(t) \} (\omega) \;=\; \int_{-\infty}^{\infty} f(t)e^{-i\omega t} dt $$

Here e^{-iωt} is the angular frequency of waves during oscillation.

## Evaluation Process of Fourier Coefficients Calculator:

The fourier calculator easily **evaluate the Fourier transform** function and gives solution in just one click. You just need to put your function (even complicated or lengthy functions) only to get result.

Let's see the steps used during the calculation process of Fourier transformation calculator. These steps are:

**Step 1**:

Identify the given function f(x) and find its limits.

**Step 2**:

Put the given function f(x) into fourier transform formula such as,

$$ F [f(t)](\omega) \;=\; \int_{-\infty}^{\infty} f(t) e^{-i \omega t} dt $$

**Step 3**:

Simplify the formula of fourier transform after adding the f(x) value if possible.

**Step 4**:

Determine 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's online calculation process.

## Pratical Example of Fourier Transform:

The practical **example of Fourier transform** function will express how to transform a Fourier function (present in the frequency domain) into a time domain function. It helps you to understand 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 transform the frequency function into the time domain function. Here are some simple steps to use this tool:

- 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 the next input box in which you transform your function.
- Review the given function before hitting the calculate button of 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 should use the load example option to learn more.
- Click on the “Recalculate” button to get a new page for solving more questions of fourier transform.

## Outcome from Fourier Calculator:

When you give input value, fourier transform calculator with steps gives you the **solution** of the given frequency function. It provides you with solutions that is:

**Result Option**:

When you click on the result option then it gives you a solution of the given problem.

**Possible Steps**:

When you click on it, this option will provide you with step by step solution with the details of all calculation process of Fourier transform.

## Benefits of Fourier Transformation Calculator:

The fourier coefficients calculator provides you multiple benefits that help you to evaluate the fourier transform online and gives solution immediately. These benefits are:

- The fourier calculator is a free-of-cost tool so you can use it for free to find fourier transform problem solutions.
- It is an
**adaptable tool**that can manage various types of fourier transform functions and convert these functions into the time domain. - Our calculator helps you to clear your concepts of the Fourier transform by solving more examples.
- It saves the time that you consume in the calculation of complex and lengthy problems of Fourier transform.
- It is a reliable tool that provides you with accurate solutions and 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.