Signal Composition and Fourier Transformation Analysis:
You need to determine the frequencies that a given periodic function, sampled N times per period, consists of. The function could represent an electric or audio signal. You need to use the FFT algorithm as discussed in class (see appendix). Recall that any periodic function of period P can be expressed as a series of sin and cos functions:
f(x)=a_0+∑_(j=1)^∞▒〖a_j cos(2πj/P t)+b_j sin(2πj/P t) 〗=
〖=a〗_0+a_1 cos(2π/P t) 〖+b〗_1 sin(2π/P t)+a_2 cos(4π/P t) 〖+b〗_2 sin(4π/P t)+⋯
If we know the period and the coefficients [a_0,a_1,b_1,a_2,b_2,a_3,b_3…] we in fact know the complete function f(t), including the frequencies it is comprised of.