Triangular frequency cutoff
= Triangular frequency cutoff
The cutoffs $\theta_n(\xi)=(1-|\xi|/n)_+$ increase pointwise to one, while their Fourier transforms are nonnegative and have integral $2\pi$ under the angular-frequency convention.
= Triangular frequency cutoff
The cutoffs $\theta_n(\xi)=(1-|\xi|/n)_+$ increase pointwise to one, while their Fourier transforms are nonnegative and have integral $2\pi$ under the angular-frequency convention.