Fast Fourier Transform
I am very new to Matlab, and I'm supposed to use the built-in FFT function to do discrete Fourier Transform for f(x) = sin x + 4 cos(5x) + (sin(6x))^2 on the interval [-pi, pi] with a uniform partition for the interval with n = 9. Then I have to
(a) Plot the magnitudes of the Fourier coefficients and
(b) Compute the first-order derivates at the grid points via FFT and compare them with f'(x).
Here's what I have for part (a):
x = -pi:0.25*pi:pi;
y = sin(x)+4*cos(5*x) + sin(6*x).*sin(6*x);
I'm a little confused with what the function fft returns. Does it return the Fourier coefficients of f(x) in my program?
-5.9965 + 2.1842i
-4.5019 - 4.8898i
0.8017 + 2.1116i
0.8017 - 2.1116i
-4.5019 + 4.8898i
-5.9965 - 2.1842i
I also don't know how to find the first-order derivates at the grid points via FFT for part (b). What function do I use?
Also, is there a way to save what I have typed on the screen, like saving the .c file when programming in C so I wouldn't have to retype the code again. The "save" command only saves my variables, but not the code. And is there a way to save just the graphs I've plotted so I can later copy them to a Word document for printing?
Thank you very much!