《信号与系统》信号总结.doc

文档介绍：Program/ Transform
Fourier Transform
Laplace Transform
Z-Transform
Definition
;
;
;
Abbreviate
,,
,
,
,
Property of ROC
The Sufficient Conditions: The Dirichlet Conditions:
1. be absolutely integrable, that is
2. have a finite number of maxima and minima within any finite interval.
3. have a finite number of discontinuities within any finite interval. Futhermore each of these discontinuities must be finite
对比傅里叶变换和傅里叶级数,有:
。

对比拉普拉斯变换和Z变换,共同点有:
收敛域的形状:平行于jw轴变换为以原点为圆心的圆。
收敛域内均不包含任何极点。
若信号在持续有限区间内有值,收敛域为整个平面。
信号为右边信号时,收敛域为极点的右边或者外边。
信号为左边信号时,收敛域为极点的左边或者里边。
信号为双边信号时,收敛域为两极点的之间的带状区域或者圆环区域。
变换域频谱为有理式时,收敛域为极点所限的区域或者趋向于无穷远处。
变换域频谱为有理式时,若信号为右边信号时,收敛域为最右边(外边)极点的右边(外边),若信号为左边信号时,收敛域为最左边(里边)极点的左边(里边)。
The ROC of consists of strip parallel to the jω-axis in the s-plane.
For rational Laplace Transfroms, the ROC doesn’t contain any poles.
If is of finite duration and is absolutely integrable, then the ROC is the entire s-plane.
If is right sided, and if the line is in the ROC, then all value of s for which will also be in the ROC.
If is left sided, and if the line is in the ROC, then all value of s for which will also be in the ROC.
If is two sided, and if the line is in the ROC, then the ROC will consist of a strip in the s-plane that includes the line .
If the Laplace Transfroms of is rational, then its ROC is bound by poles or extends to infinity. In