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# 6.10. Applying Discrete Fourier Transforms

## Problem

You'd like to use a discrete Fourier transform to analyze a dataset but aren't sure how to do so in Excel.

## Solution

Use the Fourier Analysis tool in the Analysis ToolPak.

## Discussion

Excel provides a Fourier Analysis tool as part of the Analysis ToolPak. This tool allows you to perform discrete Fourier transforms and inverse transforms directly in your spreadsheet. Once your data is transformed, you can manipulate it in either the frequency domain or time domain, as you see fit.

Consider the time series shown in Figure 6-30.

I generated this time series by superimposing several cosine and sine waves of varying frequencies. Discrete samples were taken every 0.15708 (π/20) seconds for a total of 32 samples. Figure 6-31 shows a portion of a spreadsheet containing the data making up this time series.

The first column, labeled `i`, contains an index identifying the sample number. The second column, labeled `Time`, contains the time at which each sample was taken. And the third column, labeled `Y(t)`, contains the sampled ordinate. There are a total of 32 samples, numbered 0 to 31.

### Tip

I hid several rows of data in this table so I could fit the first and last rows in one ...

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