﻿ Fast Fourier Transform
 Fast Fourier Transform

•    FFT...     Uses a Fast Fourier Transform (FFT) to calculate the frequency structure of cyclic data.  Theoretically, any waveform can be decomposed into a set of simple sine waves of different frequencies and phases.  The FFT algorithm finds these fundamental frequencies and displays them as peaks in the plot area.

Complex 'summed' frequency data occur frequently in biology (and in other areas of science).  For example, you might want to use an impedance converter to measure the heart rate in a small mammal, bird, or lizard.  Unfortunately, in addition to heart rate, you will also pick up signals produced by breathing movements.  Therefore the instrument output will contain a confusing summation of the combined effects of breathing and heart rate.  It may also contain 'noise' from random or irregular events (such as muscle movement from minor postural adjustments).

The messy-looking data shown at right are an example of such a waveform.  Although it is obviously complex, a visual inspection suggests that it does contain some regularity.  However, this periodicity is not readily studied with either the WAVEFORM or TIME SERIES operations.  Fortunately, the FFT procedure can help find the important underlying components of this complex wave.  In many cases it can detect basic cycles in a data set even if they are visually 'buried' by random noise.

The first step in the FFT procedure is selection of the size of the block of data to be analyzed.  The FFT algorithm requires that the block size be a power of two; depending on the size of your data set you can select any block size from 128 samples up to a maximum of 262,144 (256K) samples (in this example, the total number of samples in the file was about 700; accordingly, the largest possible block for FFT analysis is 512 samples).

After you select a block size, the program will show the block duration and then prompt you to go to the plot window and select the block to be analyzed.  Do this by moving the cursor into the plot area, where it will outline a block of the size you selected.  Fit the cursor block over the subset of data you wish to analyze and click the mouse once.  This will select the desired FFT block.

Once the block is chosen, you can proceed transform it (Do FFT button), select another block size ( ‘∆ interval’ ), or exit.  You may choose between showing a line or histogram plot of the results, and whether or not the results are smoothed.

After completing the FFT, the waveform's fundamental frequencies are shown graphically in the plot area.  You can examine the details of this structure by moving the cursor over the plot; the fundamental frequencies that have been 'decomposed' from the original signal, and their amplitudes, are shown numerically as peaks in the results window.

In this example, the waveform from the first image (above) is seen to be composed of three discrete fundamental frequencies, which appear as the three sharp peaks in the plot area.  The cursor is over one of the peaks, which has a frequency = .00566 Hz and a magnitude (useful for comparisons among peaks) of .13976 (these data are displayed in the results window).  You have a choice of output units (frequency in Hz, kHz, etc.; period in sec, min, etc.)

After the transform is complete, you can expand or shrink the display, or smooth (or unsmooth) the data (the results in this example are smoothed).

FFT results are stored in channel zero (not normally used by LabAnalyst); use the copy button to move them to a 'regular' data channel if you want to save them to disk (copying is only possible if the number of 'regular' channels is <40).  Alternately, you can use the 'save FFT…' button to produce an Excel-compatable spreadsheet containing the frequency data (the time units will be saved in whatever frequency or period you have selected with the popup menu) and amplitudes.

Note that if you click the exit button, you are transferred to the plot area window in channel zero (which contains the FFT results).  If you click the close box you are transferred back to the original data channel.  If you chose the former, you can switch back to the regular channels by pushing the appropriate number key, or clicking the channel selection buttons in the upper right corner of the plot area.  You cannot get back to the FFT results in channel zero except by re-running the FFT procedure.

Note that if you start the FFT procedure while using the multi-channel display mode, you'll be switched to single-channel mode (using the current active channel) prior to the beginning of analyses.  At the conclusion of the FFT calculations you'll be returned to multi-channel mode IF you click the close box or (in FP versions) the plot area.

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