查看“信号与系统”的源代码

== 信号分类 ==
== 卷积 ==
1.与单位冲激信号和单位阶跃信号的卷积

①<math>f\left ( t \right ) *\delta \left ( t \right ) =f\left ( t \right ) </math>

②<math>f\left ( t \right ) *\delta \left ( t -t_{0} \right ) =f\left ( t -t_{0} \right )</math>

③<math>f\left ( t\right ) *\delta '\left ( t \right )=f'\left ( t \right )</math>

④<math>f\left ( t\right ) *\delta ^{\left ( n \right ) } \left ( t \right )=f^{\left ( n \right ) } \left ( 
t \right )</math>

⑤<math>f\left ( t\right ) *\varepsilon \left ( t \right ) =\int_{-\infty}^{t} f\left ( \tau  \right )d\tau</math>

⑥<math>\varepsilon \left ( t \right )*\varepsilon \left ( t \right )=t\varepsilon \left ( t \right )=r\left ( t \right )</math>

⑦<math>f\left ( t \right )*r\left (t\right)=\int_{-\infty}^{t}\left [\int_{-\infty}^{k}f\left(\tau\right )d\tau\right ] dk</math>

== 傅里叶变换 ==
=== 常用信号的傅里叶变换表 ===
{| class="wikitable"
|-
|
|时域
|频域
|-
|冲激信号
|<math>\delta \left ( t \right ) </math>
|<math>1</math>
|-
|冲激偶信号
|<math>\delta '\left ( t \right ) </math>
|<math>j\omega </math>
|-
|阶跃信号
|<math>\varepsilon \left ( t \right ) </math>
|<math>\pi \delta \left (\omega \right ) +\frac{1}{j\omega } </math>
|-
|斜升信号
|<math>r\left ( t \right ) =t\varepsilon \left ( t \right ) </math>
|<math>j\pi \delta'\left ( \omega  \right ) -\frac{1}{\omega ^{2} } </math>
|-
|常数
|<math>C（直流分量）</math>
|<math>2\pi C\delta \left ( \omega  \right ) </math>
|-
|门函数
|<math>g_{\tau} \left ( t \right ) </math>
|<math>\tau Sa\left ( \frac{\omega \tau}{2}  \right ) </math>
|-
|符号函数
|<math>sgn\left ( t \right ) </math>
|<math>\frac{2}{j\omega } </math>
|-
|单边指数信号
|<math>e^{-at} \varepsilon \left ( t \right ) \;\;\left (  a>0 \right )</math>
|<math>\frac{1}{a+j\omega } </math>
|-
|双边指数信号
|<math>e^{-a\left | t \right | } \varepsilon \left ( t \right ) \;\;\left (  a>0 \right )</math>
|<math>\frac{2a}{a^{^{2} } +\omega ^{2} } </math>
|-
|复指数信号
|<math>e^{-j\omega _{0}t } </math>
|<math>2\pi \delta \left ( \omega +\omega _{0}  \right ) </math>
|-
|余弦信号
|<math>\cos \left ( w_{0}t  \right ) </math>
|<math>\pi \left [ \delta \left ( \omega +\omega _{0}  \right )+\delta \left ( \omega -\omega _{0}  \right )   \right ] </math>
|-
|正弦信号
|<math>\sin \left ( w_{0}t  \right ) </math>
|<math>j\pi \left[\delta\left(\omega+\omega_{0}\right)-\delta\left(\omega -\omega _{0} \right)\right]</math>
|-
|抽样信号
|<math>Sa\left ( at \right ) </math>
|<math>\frac{\pi }{a} g_{2a} \left ( \omega  \right ) </math>
|-
|标准一次函数
|<math>t</math>
|<math>j2\pi \delta '\left ( \omega  \right ) </math>
|-
|标准反比例函数
|<math>\frac{1}{t} </math>
|<math>-j\pi sgn\left( \omega  \right )</math>
|-
|余弦函数
|<math>\cos \left ( \omega_{0}t+\varphi  \right )</math>
|<math>\pi \left [ \delta \left ( \omega +\omega _{0}  \right ) e^{-j\varphi }+ \delta \left ( \omega -\omega _{0}  \right )e^{j\varphi }\right ] </math>
|-
|正弦函数
|<math>\sin \left ( \omega_{0}t+\varphi  \right )</math>
|<math>j\pi \left [ \delta \left ( \omega +\omega _{0}  \right ) e^{-j\varphi }-\delta \left ( \omega -\omega _{0}  \right )e^{j\varphi }\right ] </math>
|-
|冲激序列
|<math>\delta _{\tau }\left ( t \right ) =\sum_{n=-\infty}^{\infty} \delta \left ( t-nT_{1} \right ) </math>
|<math>\omega _{1} \sum_{n=-\infty}^{\infty} \delta \left ( \omega -n\omega _{1}  \right ) </math>