Using orthonormality to find Fourier series coefficients

[kolycholy]

x(t) = sigma (from m = -infinity to infinity) zm e^(j*m*omega*t)

now my book says that using orthonormality property, we can calculate zm by calculating scalar product of x(t) and em(t) (where em(t) = e^(j*m*omega*t))
hows that possible??

please feel free to move the thread if its in wrong section!

 

[Hurkyl]

Have you tried actually computing the scalar product?

 

[kolycholy]

Have you tried actually computing the scalar product?

the book has done that for me ...
it still makes no sense why zm would equal the scalar product

 

[Hurkyl]

Since you probably didn't come here just to say you're surprised, that means you don't understand something about the derivation -- so what didn't you understand?

 

[antonantal]

You are probably learning how to calculate the Fourier series coefficients. If that's the case see if this helps:
http://cnx.org/content/m10733/latest/?format=pdf