Understanding the calculation process of Excel's "Fourier analysis function" and the Fourier transform method by manual calculation

・In Japanese
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・Fourier transform
・Frequency analysis

■What is the calculation process of Excel "Fourier analysis" function

I explained the frequency analysis method using Excel's "Fourier analysis function" here. Using this Fourier analysis function, you can easily obtain the Fourier transform result. Here, in order to understand how the calculation process of the Fourier analysis function works, I explain how to actually calculate the Fourier transform one by one and perform frequency analysis.



The subject is the synthetic wave of 2 kHz and 5 kHz below. The yellow column is the result of Fourier transform using Excel functions. Calculate this same result using the Fourier transform formula.

■Fourier transform calculation result

As below. For example, when x=1 and x=5, SIN and COS are calculated respectively. Since it is necessary to obtain all x, it is necessary to perform this calculation for the number of data. The result is the same as when using the Fourier analysis function of Excel. Although SIN and COS are used this time, complex exponential function (IMEXP) can also be used.

■Frequency analysis result data

The Excel data for this analysis is here.

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