Fourier Transform using Calculator App

 Fourier Transform

To find fourier transform, input expression with respect to an independent variable and then tap ℱt

For example input expression 10 + 4.5cos(2T) + 3sin(4T) where T (time) is an independent variable.

Tap on ℱt , select independent variable as T used in expression. You also need to provide the fundamental time period TP that you want to use for the transform. For that, input start and end time values for T such that (end - start) = TP (Fundamental Time period)

Once TP is provided, the fundamental frequency for the transform will be f0=1/TP and the transform will report coefficients of frequencies in integral multiples of f0 (Harmonics)

The default value of start is 0 and end is 2pi for input in radians so that TP=2pi and f0=1/(2pi). (Frequency of sin(T)). You can also set the harmonic range to report from the transform. Default harmonic range that is reported is from 0 to 100.

Following results are reported from fourier transform.

1) Magnitude frequency plot in exponent form.

2) Magnitude frequency plot in sin cos form.

3) Table of approximate coefficients values for both exponent and sin cos form.

A snapshot is shown below of magnitude frequency plot in exponent form for the expression used above -


Fast fourier transform on spreadsheet file data

Assuming that you want to find the fast fourier transform (fft) of data in 2nd column in your spreadsheet file.

Use the ✎ option to open the variable editor. Then read the spreadsheet file using the "Read Create Spreadsheet..." option. After the file is read by the app, a page is displayed showing the variable names from 'A' to 'Z' where each variable is mapped to a specific column. 

By default, variable Y is mapped to 2nd column so we will perform fft on Y variable. Simply input the expression Y and tap on ℱt.

Case 1: You do not have a separate column for corresponding time values in spreadsheet.

In that case select independent variable as SEQ_NO and provide the value of deltaT (Time interval between two samples in sequence)


Case 2: You have a separate column for corresponding numeric time values in spreadsheet.

Assuming the 1st column in spreadsheet has the time values. Since we know that X is mapped to 1st column, select X as independent time variable. Time period will be calculated from column 1 data and rows will be sorted with respect to 1st column.

You can also use any complex expression that operates over the file data. For example to find fft of sum of 3rd and 4th columns, use the expression C+D. (By default, C is mapped to column 3 and D to column 4)

Note 1: In both the cases above it is assumed that data is sampled at equal intervals.

Note2 : To perform fft, no of input rows from spreadsheet file should be 2N. (2, 4, 8, 16 ...)

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