Challis R E, Kitney R I
Ultrasonics & Digital Signal Processing Laboratory, University of Keele, Newcastle under Lyme, UK.
Med Biol Eng Comput. 1991 Jan;29(1):1-17. doi: 10.1007/BF02446290.
This is the second in a series of four tutorial papers on biomedical signal processing, and it concerns the relationships between commonly used frequency transforms. It begins with the Fourier series and Fourier transform for continuous time signals and extends these concepts for aperiodic discrete time data and then periodic discrete time data. The Laplace transform is discussed as an extension of the Fourier transform. The z-transform is introduced and the ideas behind the chirp-z transform are described. The equivalence between the time and frequency domains is described in terms of Parseval's theorem and the theory of convolution. The use of the FFT for fast convolution and fast correlation is described for both short recordings and long recordings that must be processed in sections.
这是关于生物医学信号处理的四篇教程论文系列中的第二篇，它涉及常用频率变换之间的关系。论文首先介绍连续时间信号的傅里叶级数和傅里叶变换，并将这些概念扩展到非周期离散时间数据，然后是周期离散时间数据。文中讨论了作为傅里叶变换扩展的拉普拉斯变换。引入了z变换，并描述了线性调频z变换背后的思想。根据帕塞瓦尔定理和卷积理论描述了时域和频域之间的等效性。针对必须分段处理的短记录和长记录，介绍了使用快速傅里叶变换进行快速卷积和快速相关的方法。
