Calculus > Fourier Analysis

## What is Fourier Analysis?

Fourier Analysis is an extension of the Fourier theorem, which tells us that every function can be represented by a sum of sines and cosines from other functions. In other words, the analysis breaks down general functions into sums of simpler, trigonometric functions. The Fourier *series* tells you what the amplitude and the frequency of the sines and cosines are. Fourier Analysis is a useful tool for studying phenomena like sound or neural pathways and is commonly used in everyday items like cell phones, DVDs and JPEGs.

## Fourier Analysis Excel: Overview.

Watch the video or read the steps below:

The Analysis converts a single set of data points into a second, equal size set of data points. The Fourier analysis Excel tool has a couple of limitations:

- The maximum number of points is 4,096
- The data points
**must**be in powers of two. In other words, you can only enter 2,4,8,16,32,64,128…4,096 numbers.

If your data set contains fewer numbers (i.e. 5 or 30), pad the data set with extra zeros (to make 8 or 32) so that you can run the Fourier analysis tool.

### How to run Fourier Analysis Excel 2013: Steps

1st: Type your data into a single column (it only works on a single column of Data).

2nc: Click the “Data” tab and then click “Data Analysis.” If you don’t see that option, load the Data Analysis Toolpak.

3rd: Click “Fourier Analysis” and then click “OK.”

4th: Type a range for your data into the Input Range box. For example, if your data is in cells J1 to J16, type “J1:J16” into that box.

5th: Check the “Labels in first row” box if you have column headers (so that Excel knows to exclude that row).

6th: Click in the Output Range box and then select an area immediately to the right of your data. You can also check “New Worksheet,” but having the Fourier Analysis results right next to your data will be more useful.

7th: Check the “Inverse” box only if you have results from a prior analysis and you want to find the original function.

8th: Click “OK.”

**Tip: **An “i” in the results means a complex number. If you see a green triangle, it means the data has been converted to text. Click the cell, click the error message and choose “Convert to Number.”

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Thank you very much. However, I am not sure how to take the imaginary numbers after the analysis and turn them into meaningful PSD values for various frequency ranges. Can you help me with this or point me to additional resources? Thanks so much, Thomas

Hi, Thomas,

Sorry, but Power Spectral Density (PSD) is outside my area of expertise. Perhaps try a physics forum? If you do find an answer, perhaps you’d consider coming back here and posting it :)

Best of luck,

Stephanie