Time for action - using the fft function

1. 1. Let us try to Fourier transform the function:

(7.17)

• where t ∈ [0; 2π] using 150 data points. This function is characterized by two different frequencies (or modes) that will show in the Fourier transformation as two distinct peaks.

²This is also referred to as an O(N²) algorithm. O is pronounced 'big-O'.

1. 2. To generate the data we use:

octave:29> N=150; t = linspace(0,2*pi, N);
octave:30> f = sin(2*t) + 2*sin(5*t);

1. 3. Then we simply transform those data via:

octave:31> F = fft(f);

1. 4. The complex vector F is not really of much information itself, so we often display the absolute value (or magnitude) of the elements in the array:

octave:32> plot(abs(F), "o-")

• which produces the plot seen in the figure below:

What just happened?

In Commands 29 and 30, we generated the data set. I strongly recommend that you try to plot f versus t to see the function that we are transforming. We then call fft and plot the absolute value of the transformed data...