Transformada Discreta de Fourier Utilizando el Asistente de NumXL

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Hello and welcome to another tutorial for NumXL 1.6. In this video we'll demonstrate the use of Discrete Fourier Transform wizard. To get us started we've generated a random sample of 25 observations.

First select an empty cell in your worksheet where you wish for the output to be displayed, then click on the four-year icon in the NumXL toolbar.

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The Discrete Fourier Transform wizard pops up. Notice that the output field is set to the current active cell in your worksheet. Now let's select the input data. You can include the header in your selection if you wish, then select the remaining cells in the column J.

Notice that the options and missing values tabs become enabled. Click on the options tab.

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By default the frequency component output is checked as well as the amplitude and phase. The number of components is set to 1. Finally the input variable output is unchecked. Let's leave it unselected for now, but let's change the number of components to 7 for our demonstration. Next, click on the missing values.

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In this tab the default is "Don't Accept Missing Values", this is fine for our demonstration, so let's leave it checked. Now click OK.

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The Discrete Fourier Transform wizard generates a table for the first seven frequency components, amplitude and phase angle. Let's plot the amplitudes for the different components. 

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We can see from the graph that the components exhibit comparable values. Now let's plot the filtered data using a subset of the frequency spectrum. Again select an empty cell in your worksheet and click on the Fourier icon in the NumXL tab.

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Select the input data range and switch to the options tab. This time uncheck the frequency component output selection and select the input variable output. For now let's choose two frequency components to recreate the input variable. This can be changed later on from the input table.

Next, switch to the missing values tab.

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Like previously, let's leave the default missing values treatment unchanged, click OK.

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The wizard generates a filtered version of the input dataset. Now let's plot the filter time series and compare them with the original data.

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Next let's change the number of components and examine the filtered signal. Go to the first cell in the max component column and change its value to 1.

The filtered signal represents the average of the input data.

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Let's again go to the first cell in the max component column and edit its value to 2.

The filtered signal now includes the average and the first principal frequency component.

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Now let's do the same thing and change the value to 4.

You can notice that the filtered signal is getting closer to the original signal. Next let's change the value to five, now to nine, and finally when we pick 13 components, we can recover the original input signal in this entirety. 

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That is it for now, thank you for watching!