Hi.
I did a course last year on Signals and Systems, as a part my Electrical Engineering, which is altogether based on Fourier transforms and Fourier series. This was followed by a theoretical and lab course on Communication Theory, which relied on these concepts heavily and my understanding of these concepts got refined. After these three courses, I feel very apt for teaching you these concepts. Believe it or not, I got an O in all three courses(O is the top grade at my university). This was mainly because I really like mathematics. I myself always aim to understand the complete mathematical theory of every subject before even thinking of experimental/application part. I'm more of a theoretical guy in that aspect.
Since your aim is to write a C++ code, I would also be happy to help you during the debugging process. I myself recently finished writing a huge code, and I know how debugging can be a big pain.
I think I should be able to teach you the theoretical concepts with visual understanding of fourier transform and fourier series in 2-5 sessions, depending upon your preference in learning the topic or urgency in being able to write the code.
Now, as to why I offer such a cheap price is because this is my first day at 'Freelancers', and I'm exploring this new thing. I would love to have this job. Also, I like to teach people, and that's why I usually take up teaching assistant jobs every semester.