- #1
errordude
- 17
- 0
suppose, [tex] s_{n}(f;t) = \sum_{k=-n}^{n}\widehat{f}(k)e^{ikt}[/tex]
and
[tex]\sigma_{N}(f;t)= \frac{1}{N+1}\sum_{n=0}^{N}s_{n}(f;t)[/tex].
how do i get from this [tex]\sigma_{N}(f;t)= \frac{1}{N+1}\sum_{n=0}^{N}s_{n}(f;t)[/tex].
to this
[tex]\sigma_{N}(f;t)= \sum_{n=-N}^{N}(1-\frac{|n|}{N+1})\widehat{f}(n)e^{int}[/tex]
obviously one starts with:
[tex]\sigma_{N}(f;t)=\frac{1}{N+1}\sum_{n=0}^{N}\sum_{k=-n}^{n}\widehat{f}(k)e^{ikt}[/tex]
thanks!
and
[tex]\sigma_{N}(f;t)= \frac{1}{N+1}\sum_{n=0}^{N}s_{n}(f;t)[/tex].
how do i get from this [tex]\sigma_{N}(f;t)= \frac{1}{N+1}\sum_{n=0}^{N}s_{n}(f;t)[/tex].
to this
[tex]\sigma_{N}(f;t)= \sum_{n=-N}^{N}(1-\frac{|n|}{N+1})\widehat{f}(n)e^{int}[/tex]
obviously one starts with:
[tex]\sigma_{N}(f;t)=\frac{1}{N+1}\sum_{n=0}^{N}\sum_{k=-n}^{n}\widehat{f}(k)e^{ikt}[/tex]
thanks!