标题： 多维二次相位傅里叶变换：理论分析与应用 显示英文标题

标题： The Multidimensional Quadratic Phase Fourier Transform: Theoretical Analysis and Applications

摘要： 二次相位傅里叶变换（QPFT）是一些众所周知的积分变换的一般化，包括线性canonical变换（LCT）、分数傅里叶变换（FrFT）和傅里叶变换（FT）。 本文介绍了多维QPFT，并研究了其理论性质，包括Parseval恒等式和反演定理。 在QPFT框架内提出了多变量的广义卷积和相关性，扩展了单一变量函数的传统卷积。 此外，建立了多维QPFT的Boas型定理。 作为应用，探索了利用所提出的卷积运算进行乘法滤波器设计以及求解积分方程。 显示英文摘要

摘要： The quadratic phase Fourier transform (QPFT) is a generalization of several well-known integral transforms, including the linear canonical transform (LCT), fractional Fourier transform (FrFT), and Fourier transform (FT). This paper introduces the multidimensional QPFT and investigates its theoretical properties, including Parseval's identity and inversion theorems. Generalized convolutions and correlation for multiple variables, extending the conventional convolution for single-variable functions, are proposed within the QPFT setting. Additionally, a Boas-type theorem for the multidimensional QPFT is established. As applications, multiplicative filter design and the solution of integral equations using the proposed convolution operation are explored.