# 单边带调制

（重定向自单边带

SSB · DSB
FMPM

OOK · QAM
FSK
MSK · GFSK
PSK
CPM

CSS · DSSS · THSS · FHSS

## 数学表述

${\displaystyle s_{\text{ssb}}(t)=s(t)\cdot \cos(2\pi f_{0}t)-{\widehat {s}}(t)\cdot \sin(2\pi f_{0}t),\,}$

(Eq.1)

${\displaystyle s(t)={\tfrac {1}{2}}\underbrace {(s(t)+j\cdot {\widehat {s}}(t))} _{s_{a}(t)}+{\tfrac {1}{2}}\underbrace {(s(t)-j\cdot {\widehat {s}}(t))} _{s_{a}^{*}(t)},}$

${\displaystyle {\tfrac {1}{2}}S_{\mathrm {a} }(f)={\begin{cases}S(f),&{\text{for}}\ f>0,\\0,&{\text{for}}\ f<0,\end{cases}}}$

${\displaystyle {\mathcal {F}}^{-1}\{S_{\mathrm {a} }(f-f_{0})\}=s_{a}(t)\cdot e^{j2\pi f_{0}t}=s_{\text{ssb}}(t)+j\cdot {\widehat {s}}_{\text{ssb}}(t).\,}$

{\displaystyle {\begin{aligned}s_{ssb}(t)&=Re{\big \{}s_{a}(t)\cdot e^{j2\pi f_{0}t}{\big \}}\\&=Re\left\{\ [s(t)+j\cdot {\widehat {s}}(t)]\cdot [\cos(2\pi f_{0}t)+j\cdot \sin(2\pi f_{0}t)]\ \right\}\\&=s(t)\cdot \cos(2\pi f_{0}t)-{\widehat {s}}(t)\cdot \sin(2\pi f_{0}t).\end{aligned}}}

### 下边带

${\displaystyle s(t)}$ 也可以作为复共轭 ${\displaystyle s_{a}^{*}(t)}$ 的实部来恢复，该复共轭表示 ${\displaystyle S(f)}$ 的负频率部分。当 ${\displaystyle f_{0}\,}$ 足够大时，${\displaystyle S(f-f_{0})}$ 没有负频率，乘积 ${\displaystyle s_{a}^{*}(t)\cdot e^{j2\pi f_{0}t}}$ 是另一个解析信号，它的实部是真正的低边带传输：

{\displaystyle {\begin{aligned}s_{a}^{*}(t)\cdot e^{j2\pi f_{0}t}&=s_{\text{lsb}}(t)+j\cdot {\widehat {s}}_{\text{lsb}}(t)\\s_{lsb}(t)&=Re{\big \{}s_{a}^{*}(t)\cdot e^{j2\pi f_{0}t}{\big \}}\\&=s(t)\cdot \cos(2\pi f_{0}t)+{\widehat {s}}(t)\cdot \sin(2\pi f_{0}t).\end{aligned}}}

${\displaystyle 2s(t)\cdot \cos(2\pi f_{0}t),\,}$

## 参考资料

1. ^ US 1449382 John Carson/AT&T: "Method and Means for Signaling with High Frequency Waves" filed on December 1, 1915; granted on March 27, 1923
2. ^ The History of Single Sideband Modulation 互联网档案馆存档，存档日期2004-01-03., Ing. Peter Weber
3. ^
4. ^ History Of Undersea Cables, (1927)
5. ^ Tretter, Steven A. Chapter 7, Eq 7.9. (编) Lucky, R.W. Communication System Design Using DSP Algorithms. New York: Springer. 1995: 80. ISBN 0306450321.

## 延伸阅读

• Sgrignoli, G., W. Bretl, R. and Citta. (1995). "VSB modulation used for terrestrial and cable broadcasts." IEEE Transactions on Consumer Electronics. v. 41, issue 3, p. 367 - 382.
• J. Brittain, (1992). "Scanning the past: Ralph V.L. Hartley", Proc. IEEE, vol.80,p. 463.
• eSSB - Extended Single Sideband