论文标题
自由跨度转换及其应用的卷积定理
Convolution theorems for the free metaplectic transformation and its application
论文作者
论文摘要
自由跨度转换（FMT）广泛用于许多领域，例如滤波器设计，图案识别，图像处理和光学。为了获得更简洁，更直观的卷积形式，本文研究了FMT域中的两种新的卷积定理。首先，基于广义翻译的表达，我们在FMT域中得出了第一类的卷积定理，该定理具有优雅和简单性，可与傅立叶变换（FT）的经典结果相媲美。其次，我们再次在FMT领域中给出第二种卷积定理，以进一步研究卷积理论的多样性。它具有一个优势，它可以用简单的积分来表示，并且在乘以过滤器设计中易于实现。最后，基于上述卷积定理的简单形式，我们讨论了MFT域中的乘法过滤器。
The free metaplectic transformation (FMT) is widely used in many fields such as filter design, pattern recognition, image processing and optics. In order to obtain a more concise and intuitive convolution form, this paper studies two kinds of new convolution theorems in the FMT domain. First, based on the expression of the generalized translation, we derive the convolution theorem of the first kind in the FMT domain, which has elegance and simplicity comparable to the classical results of Fourier transform (FT). Second, we again give the convolution theorem of the second kind in the FMT domain to further study the diversity of convolution theory. It has the advantage that it can be represented by a simple integral and is easy to implement in multiplying filter designs. Finally, based on the simple form of the above convolution theorems, we discuss multiplicative filters in the MFT domain.
