Understanding the Discrete Fourier Transform

Question

I have a small query regarding discrete Fourier transforms. If I understand correctly, then we do the conversion of the polynomial into its representation of a point value, with n points for a polynomial that rises to the degree n-1. But why should we evaluate it on the nth roots of unity? Isn't there any other n points that uniquely identify this polynomial? And much simpler?

Answer 1

Won't other n points uniquely identify this polynomial? And much easier?

. 1) , n , 2) . : ?

Answer 2

• .
• ( n O (n log n)).
• .

- , . ( )

Answer 3

, . . ( ) . , :

(1) - , .

(2) ( ) -   , , - ( ). , .

(3) , , - , , - , N ^ 2, N log N.

Answer 4

"" . , - - .

• http://betterexplained.com/articles/an-interactive-guide-to-the-fourier-transform/

• http://www.altdevblogaday.com/2011/05/17/understanding-the-fourier-transform/