I have a integral $$ f(u)= \int_{-n/2}^{n/2} \int_{-n/2}^{n/2} e^{j u \pi ((x^2+y^2)- (ax+by)^2) } d_x d_y,$$ where $n>0,u>0$, and $a , b \in [0,1]$. I want to find the range of $u$ to make $ |f(u) | \leq \beta$, where $\beta$ is a given threshold. How can I simplify it? Could anyone give some hints, textbooks, or comments? Thanks very much!
2026-02-23 09:11:22.1771837882
How to calculate this integral to find the range of u?
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