FFT Algorithms - Matlab

        If you use Matlab to get the FFT you could use an m-file like the one below.

Data=dlmread('SensorSignal1.txt','\t');

Time = Data(:,1);

VData = Data(:,2);

plot(Time,VData)

pause

SigFFT = fft(VData);

plot(abs(SigFFT))

        This m-file does the following:

• Data=dlmread('SensorSignal1.txt','\t');

  • Brings the data from the file SensorSignal1.txt into the Matlab workspace.
  • The file is "tab-delimited" - denoted by '\t'.  Other delimiters are possible, e.g. commas, but they don't specify how to treat them in the help within Matlab.
  • The file should be a pure text file, and that's the kind of file many data acquisition programs generate, even if they use other extensions like ".dat"
  • You need to set the "path" so that the m-file is at a location where Matlab can find it.

• Time = Data(:,1);

• VData = Data(:,2);

  • Separates the data into two one-dimensional arrays.  This assumes that the original data file, SensorSignal1.txt, has both time and data in two columns.
  • You need the data in a separate array because the FFT function can only handle a one-dimensional array.
  • Then, plot the data vs time.  This gives you a chance to look to see if things are OK.

• SigFFT = fft(VData);

  • This is the place where the FFT is calculated.
  • There are other "versions" of the FFT algorithm, IFFT, FFT2, IFFT2, and FFTSHIFT.  Check the help for information about them.
  • The fft function returns a complex array.  The reals are the a's, and the complex values are the b's in the Fourier expansion.

• plot(abs(SigFFT))

  • This plots the c's for the FFT that was calculated.  If you want the a's and b's, you can extract the real and the imaginary parts to get what you want.  There are two notes that give you info on the c's.

Precautions:

• The m-file code above can be copied directly from the page, pasted into an editor and saved.  We have put it on the left edge of the page to minimize possible problems with indentations, etc.

• When you save the m-file be sure that you have the path to the m-file included in the path settings.  Use File-Set Path to add the path if necessary.

Points to note:

• Matlab indices start at 1, but we start with a coefficient, a_o.  The first coefficient is a_o and it will be stored in the first element of the array (SigFFT in the example m-file), i.e, SigFFT(1).  Every other element in the array is also off by 1.  For example, SigFFT(12) will contain the 11^th harmonic.

• The calculation will be done in terms of the harmonics of the fundamental frequency of the data set.  If you have a square wave that shows two periods in the data set, the first harmonic of the square wave will be the second harmonic of the fundamental frequency of the data set, and - given the first point just above - will appear in the third element of the FFT array.

  • When you do the calculation, you will often have data that has many periods in one data set.  Those frequencies - in the periodice signal - will be at exact multiples of the fundamental frequency of the data set (a sharp line in the computed FFT) or near a multiple (a spread-out line).  You shouldn't expect the fundamental of a periodice signal to be the fundamental frequency of the data set unless you have exactly one period of your periodic signal in the data set.

  • Example:  You have a data set that is 2 milliseconds long.  The fundamental frequency of the data set is 0.5 kHz (= 500 Hz).  If you have a one kHz signal embedded in that data, it will be at the second harmonic of the 500 Hz.  (In Matlab, that will be at the index = 3.)

  • The second biggest problem with doing the FFT in Matlab is getting the index straight.

• The calculation does not include the 2/N term.  You have to compensate for that.  In a five volt square wave with 4000 data points, the first harmonic of the square wave will calculate out at a magnitude of 12,813.  The actual first harmonic (i.e., the fundamental) of a square wave of amplitude A is 4A/p, and that would calculate out to about 6.4.  To get from 12,813 to 6.4 you need to multiply 12,813 by 2/4000 (that's 2/N).

  • The biggest problem with doing the FFT in Matlab is getting the correlation between the results that are returned and the actual numbers you want.