I'm confused by what the professor means on this Fourier Series proble

[Jamin2112]

Homework Statement

See the second bullet point on this page: http://facweb.northseattle.edu/rjenne/e240w13flr/hwflr/feb21/e240w13hwfeb21.pdf

Homework Equations

So I know that fft(x) for a bunch of sample points x={x₁, x₂, ..., x_n} returns the n Fourier coefficients for a function fitted through those sample points.

The Attempt at a Solution

So I'm a little confused about what the 1/31 and the c mean in the context of this problem. What I'm trying to do, ultimately, is use the Fast Fourier Transform algorithm on 31 equally spaced sample points on the domain [1, 4] to reconstruct the function on 3001 equally spaced sample points on the same domain.

Thoughts?

 

[DrClaude]

So I know that fft(x) for a bunch of sample points x={x₁, x₂, ..., x_n} returns the n Fourier coefficients for a function fitted through those sample points.

[...]

So I'm a little confused about what the 1/31 and the c mean in the context of this problem.

How is the Fourier transform normalized? And can you see any link between what I put in bold there?

 

[Jamin2112]

How is the Fourier transform normalized? And can you see any link between what I put in bold there?

Now I've figured out that problem, but I'm confused on a different problem where I have to use the MATLAB function odeset to change absolute and relative tolerance. Do you know how to do that?