Example of a Fourier Series ApproximationĪ Sawtooth function, with period 1 and peak-to-peak amplitude of 1 can be represented fairly well by the Fourier series The period can be replaced by one of arbitrary length, with the only issue being that the formulas will become a little more complicated to work with (Jackson, 2004).įourier series are useful in a wide range of fields including acoustics, with representation of musical sounds as sums of waves of various frequencies (Nearing, 2020) or quantum mechanics, for the quantum wave function of a particle in a box. Therefore, the sum of the series also has a period of 2π. Click the cell, click the error message and choose “Convert to Number.”Īny periodic function can be represented by a Fourier Series- a sum (an infinite series) of sines and cosines:į(x) = A 0 a 1 cos x + a 2 cos 2x +… + b 1 sin x + b 2 sin 2x +…Įach term is a periodic function with period 2π. If you see a green triangle, it means the data has been converted to text. Tip: An “i” in the results means a complex number. Step 7: Check the “Inverse” box only if you have results from a prior analysis and you want to find the original function. You can also check “New Worksheet,” but having the Fourier Analysis results right next to your data will be more useful. Step 6: Click in the Output Range box and then select an area immediately to the right of your data. Step 5: Check the “Labels in first row” box if you have column headers (so that Excel knows to exclude that row). For example, if your data is in cells J1 to J16, type “J1:J16” into that box. Step 4: Type a range for your data into the Input Range box. Step 3: Click “Fourier Analysis” and then click “OK.” Step 2: Click the “Data” tab and then click “Data Analysis.” If you don’t see that option, load the Data Analysis Toolpak. Step 1: Type your data into a single column (it only works on a single column of Data). How to run Fourier Analysis Excel 2013 & Newer: Steps 5 or 30), pad the data set with extra zeros (to make 8 or 32) so that you can run the Fourier analysis tool. If your data set contains fewer numbers (i.e.
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