1. 傅里叶级数(Fourier series) 2 从傅里叶级数到傅里叶变换的严格推导 3 傅里叶变换(Fourier transform) 4 傅里叶变换基本性质 5 傅里叶变换基本性质证明 为什么需要傅里叶变换,从波形处理的角度讲,若只看时间域,各频率耦合在一起,难以看出波的特征。此时,若将其转换到频率域,观察其频谱,则易看出其特点...
1. 傅里叶级数(Fourier series) 2 从傅里叶级数到傅里叶变换的严格推导 3 傅里叶变换(Fourier transform) 4 傅里叶变换基本性质 5 傅里叶变换基本性质证明 为什么需要傅里叶变换,从波形处理的角度讲,若只看时间域,各频率耦合在一起,难以看出波的特征。此时,若将其转换到频率域,观察其频谱,则易看出其特点...
傅里叶变换对于波形处理至关重要，它能够将信号从时间域转换到频率域，使我们能够直观地观察和理解信号的频率特性，而非仅依赖于时间序列的复杂耦合。这一转换思想的核心在于从一种域到另一种域的转化，使得某些计算（如偏微分方程的求解）在频率波数域变得极为简单，而信号的特征在频率域也更加清晰。傅...
Extended Gevrey Regularity via the Short-Time Fourier Transform We study the regularity of smooth functions whose derivatives are dominated by sequences of the form \\(M_p^{au ,\\sigma }=p^{au p^{\\sigma }}\\), τ > 0, σ≥ 1. We show that such functions can be characterized thr...
In summary, the Fourier transform is a generalization of the Fourier series in the limit as L approaches infinity. It replaces the discrete coefficients A_n with a continuous function F(k)dk and changes the sum to an integral. This allows for the transformation of a discrete variable to a...
The aim of this paper is to deduce the expressions for the fourier transform pair and the Laplace transform pair from the familiar expression of the Fourier Series. This may help to understand the underlying implications of the processes.
Bioinspired multi-compartment architectures are desired in synthetic biology and metabolic engineering, as credited by their cell-like structures and intrinsic ability of assembling catalytic species for spatiotemporal control over cascade reactions like
In prebiotic evolution, self-replicating molecules are believed to have evolved into complex living systems by expanding their information and functions open-endedly. Theoretically, such evolutionary complexification could occur through successive appear
Since its introduction to industrial settings in the mid-1990s, Raman spectroscopy based on modern dispersive instrumentation has been used to solve identification, quantification, and process monitoring problems. The first applications were closely linked to those already analyzed by Fourier-transform ...
The course is taught from the mathematics perspective and is focused on the properties of continuous and discrete signals and systems, Fourier series and Fourier transform, and Laplace-transform. The second course is taught to the first-year students and is focused on object-oriented programming (...