- #1
baby_1
- 159
- 15
Hi,
First of all, I want to say that I know how can define and calculate Fourier coefficients but I have some question about the final presentation of Fourier and half-period or unknown period functions.
1)In this function how can we define T?
2)for above diagram, in a book, they define f(t) as
f(t)=cos(at)-(1/3)cos(3at)+...
but my question is, Isn't the function f(t) even? but the original shape is odd?
how would it be possible that we present a Sin function into Cos functions?
because for odd function we have a Fourier series like
[tex]f(t)=\sum_{n=1}^{\infty}B_{n}Sin(\omega_{0}((2n+1)t)=B_{0}Sin(\omega_{0}t)+B_{0}Sin(3\omega_{0}t)+...[/tex]
3)why in most references the writer prefer to write even function for half-range expansion instead of odd half-range expansion of a real systems?
Thanks
First of all, I want to say that I know how can define and calculate Fourier coefficients but I have some question about the final presentation of Fourier and half-period or unknown period functions.
1)In this function how can we define T?
2)for above diagram, in a book, they define f(t) as
f(t)=cos(at)-(1/3)cos(3at)+...
but my question is, Isn't the function f(t) even? but the original shape is odd?
how would it be possible that we present a Sin function into Cos functions?
because for odd function we have a Fourier series like
[tex]f(t)=\sum_{n=1}^{\infty}B_{n}Sin(\omega_{0}((2n+1)t)=B_{0}Sin(\omega_{0}t)+B_{0}Sin(3\omega_{0}t)+...[/tex]
3)why in most references the writer prefer to write even function for half-range expansion instead of odd half-range expansion of a real systems?
Thanks