Let , the partial sum operator of fourier series can be represented by

actually

Since , for , then behavior much like Hilbert transform

(a) ,

(b)

By the fact in this post, in

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when time goes to infinity

Let , the partial sum operator of fourier series can be represented by

actually

Since , for , then behavior much like Hilbert transform

(a) ,

(b)

By the fact in this post, in

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