一、问题的提出 二、三角级数三角函数系的正交性 三、函数展开成傅里叶级数 四、小结思考题

一、掌握红外光谱区域的划分;了解红外光谱法的特点。 二、了解红外光谱吸收的产生条件;掌握双原子、多原子分子的振动。 三、掌握常用官能团的特征吸收频率,能识别简单化合物的红外光谱图 四、了解色散型和Fourier变换红外光谱仪的结构及其差异性

Exercise for home study O&W4.47 tea this problem examines the Fourier transform of a continuous-time LTI system with a real, causal impulse response, h(t) (a) To prove that H(w) is completely specified by eh(u) for a real and causal h(t) lore the even part of a function, he(t)

Directions: The exam consists of 5 problems on pages 2 to 19 and work space on pages 20 and 21. Please make sure you have all the pages. Tables of Fourier series properties are supplied to you at the end of this booklet. Enter all your work and you answers directly in the spaces provided on the printed pages of this booklet

PROBLEM SET 11 SOLUTIONS Problem 1(O&W 1029(d)) In this problem we are asked to sketch the magnitude of the Fourier transform associated with the pole-zero diagram, Figure P10.29(d). In order to do so, we need to make some

Home Study Exercise (E1)O&W3.46(a)and(c) (t) and y(t) are continuous-time periodic signals with a period= To and Fourier series representations given b

Convergence Issues Synthesis equation: None. since integrating over a finite interval Analysis Equation: Need conditions analogous to CTFT, e. g

Convolution Property 0(t)=h(t)*(t)←→Y(j)=H(ju)X( where h(t)←→H(ju) A consequence of the eigenfunction property

Another(important! ) example: Periodic Impulse train n(t)=∑(t Sampling function important for sampling .2T

8.1基本空间 8.1.1引言 偏微分方程的古典理论对解的光滑性要求过高,这不仅 仅常常不合实际问题的要求,而且影响理论的进一步发展。 我们希望对一般的方程及定解问题统一地扩充解地概念。这 首先需要扩充函数地概念。 Fourier变换是求解偏微分方程诸多问题的有力工具。但 是能做此变换的函数是不多的。我们希望扩广它的使用 范围,从而需要扩充函数的概念。 当物理学家为了量子力学的需要引入函数(x)时 ,数学和物理的紧密关系便出现了裂痕