- #1
sridhar10chitta
- 28
- 0
There are two functions f(t) and g(t); t is the independent variable.
The distance between the two functions will be given by [1/2pi integral{f(t)-g(t)}^2 dt]^1/2 between -pi and +pi.
Apparently, this distance also is the Fourier coefficient of each term in the Fourier
expansion of a periodic function f(t) such that it is closest to f(t).
Why is this so ?
why is not the distance given by f(t)-g(t) simply ?
i.e 1/sqrt(2pi) integral{f(t)-g(t)}dt between -pi and +pi.
The distance between the two functions will be given by [1/2pi integral{f(t)-g(t)}^2 dt]^1/2 between -pi and +pi.
Apparently, this distance also is the Fourier coefficient of each term in the Fourier
expansion of a periodic function f(t) such that it is closest to f(t).
Why is this so ?
why is not the distance given by f(t)-g(t) simply ?
i.e 1/sqrt(2pi) integral{f(t)-g(t)}dt between -pi and +pi.