## 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 & Newer: Steps

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

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

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

Step 4: 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.

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

Step 6: 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.

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

Step 8: 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.”

Check out our YouTube channel for more help and tips!

**CITE THIS AS:**

**Stephanie Glen**. "Fourier Analysis: Definition, Steps in Excel" From

**CalculusHowTo.com**: Calculus for the rest of us! https://www.calculushowto.com/fourier-analysis-definition-excel/

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I expect that the output complex result requires determining the absolute value, separating the real part and the absolute part and normalizing by the amplitude to obtain Acos(w) and Bcos(w) and the bandwidth is 2/N

I will check this out. I wish you had a direct example as to how to use the result.

From the results of complex numbers, if i calculate the angle phi, it does not match with the required results. Please clarify on this issue

Prakash,

Can you please give an example of your input and the “required” results. I’ll take a look. Thank you.

I’m running MS Excel 2013. It appears that the first result value (DC offset) must be divided by the Total Number of Samples to get the correct Magnitude. Also, each remaining result must be divided by 1/2 the Total Number of Samples. Except for the DC Offset, the results with the correct phasing appear to be in the last half of the results.