# Fourier Transformation (RapidMiner Studio Core)

## Synopsis

This operator uses the label as a function of each attribute and calculates the Fourier transformations as new attributes.## Description

The Fourier Transformation operator creates a new ExampleSet consisting of the result of a Fourier transformation for each attribute of the input ExampleSet. This operator uses the label as a function of each attribute and calculates the Fourier transformations as new attributes. The Fourier transformation is a mathematical transform with many applications in physics and engineering. Very commonly, it expresses a mathematical function of time as a function of frequency, known as its frequency spectrum. The Fourier inversion theorem details this relationship. For instance, the transform of a musical chord made up of pure notes (without overtones) expressed as amplitude as a function of time, is a mathematical representation of the amplitudes and phases of the individual notes that make it up. The function of time is often called the time domain representation, and the frequency spectrum the frequency domain representation. The inverse Fourier transform expresses a frequency domain function in the time domain.

## Input

- example set input (Data Table)
This input port expects an ExampleSet. It is output of the Generate Data operator in the attached Example Process.

## Output

- example set output (Data Table)
The Fourier Transformation is performed and the resultant ExampleSet is returned through this port.

- original (Data Table)
The ExampleSet that was given as input is passed without changing to the output through this port. This is usually used to reuse the same ExampleSet in further operators or to view the ExampleSet in the Results Workspace.

## Tutorial Processes

### Introduction to the Fourier Transformation operator

The Generate Data operator provides a sample ExampleSet. A breakpoint is inserted here so that you can have a look at the ExampleSet. You can see that the ExampleSet has three real attributes i.e. att1, att2 and att3. The Fourier Transformation operator is applied on this ExampleSet. The Fourier Transformation operator creates a new ExampleSet consisting of the result of a fourier transformation for each attribute of the given ExampleSet. This operator uses the label as a function of each attribute and calculates the fourier transformations as new attributes. The resultant ExampleSet can be seen in the Results Workspace.