Here's an equation of the Fourier transform:
Fourier Equation
In the same equation image above, in the second line, is an equation I read from a paper. It seems that the
a_n and
b_n are turned into functions of
A(u) and
B(u) respectively, which depend on the variable
u, which is the frequency. There is also an additional
2*pi in the
sin and
cos functions.
In other words, the eventual equation can get to become:
New Equation
I don't understand several things in this new equation.
First, what are the A(u) and B(u) functions? Why do they depend on u?
Second, why is there a 2*pi in the sin and cos functions? What do the 2*pi mean?
Third, how does the new equation differ from the original equation?
\frac{a_0}{2} + \sum_{n=1}^\infty a_n \cos(nx) + b_n \sin(nx)
above line not rendered very well. Try
f(x) = a_0/2 + sum (from n = 0 to infinity)(a_n cos(nx) + b_n sin(nx)