# Fourier Analysis

Calculates the frequency-domain representation of a finite time series in time domain.

## Fourier Analysis with NumXL

Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions. Fourier analysis grew from the study of Fourier series, and is named after Joseph Fourier, who showed that representing a function as a sum of trigonometric functions greatly simplifies the study of heat transfer.

Today, the subject of Fourier analysis encompasses a vast spectrum of mathematics. In the sciences and engineering, the process of decomposing a function into oscillatory components is often called Fourier analysis, while the operation of rebuilding the function from these pieces is known as Fourier synthesis (aka inverse).

For time series analysis, a special version of the Fourier transform is used: Discrete Fourier Transform. The DFT transformation from the time domain to the frequency domain is the most important discrete transform in many practical applications, and it is completely reversible: the original signal can be reconstructed as a function of time by computing the inverse Discrete Fourier transform (IDFT).

NumXL functions does all the heavy lifting for you: calculate the frequency spectrum and/or reconstructing (original) time series using whole or subset of the frequency components, leaving you the important tasks of interpreting the actual results and applying intuition.

## Fourier Analysis Function

Discrete Fourier Transform (DFT)

This is the first tutorial in our ongoing series on time series spectral analysis. In this entry, we will c...