svensl
Full Member level 1
Consider a sequence (an) that is uniformly distributed modulo 1.
We know from the equidistribution theorem that:
N--> infinity 1/N Σ[ f((a•n mod 1) ) ,n=1..N] can be re-written as ∫(f(x)dx, x=0,1).
See, www.en.wikipedia.org/wiki/Equidistribution_theorem
In my case I also have a modulo 1 sequence a•n in the sum, but the sequence is also multiplied by an exponential function exp(-i omega n T):
N-->infinity 1/N Σ[ (a*n mod 1)exp(-i omega n T), n=1..N]. Can anyone help me simplify this? I am sure there are some theorems that might help me with this problem.
Thanks,
Sven
We know from the equidistribution theorem that:
N--> infinity 1/N Σ[ f((a•n mod 1) ) ,n=1..N] can be re-written as ∫(f(x)dx, x=0,1).
See, www.en.wikipedia.org/wiki/Equidistribution_theorem
In my case I also have a modulo 1 sequence a•n in the sum, but the sequence is also multiplied by an exponential function exp(-i omega n T):
N-->infinity 1/N Σ[ (a*n mod 1)exp(-i omega n T), n=1..N]. Can anyone help me simplify this? I am sure there are some theorems that might help me with this problem.
Thanks,
Sven
