# 最小频移键控

SSB · DSB
FMPM

OOK · QAM
FSK
MSK · GFSK
PSK
CPM

CSS · DSSS · THSS · FHSS

## 数学表达

MSK的调制信号可以表达为：${\displaystyle s(t)=a_{I}(t)\cos {\left({\frac {{\pi }t}{2T}}\right)}\cos {(2{\pi }f_{c}t)}-a_{Q}(t)\sin {\left({\frac {{\pi }t}{2T}}\right)}\sin {\left(2{\pi }f_{c}t\right)}}$

${\displaystyle a_{I}(t)}$${\displaystyle a_{Q}(t)}$ 代表周期为 2T 的奇偶位信息序列所产生的矩形波形。运用三角变换，此表达可以转换成频率和相位调制更明显的形式。

${\displaystyle s(t)=\cos[2\pi f_{c}t+b_{k}(t){\frac {\pi t}{2T}}+\phi _{k}]}$

${\displaystyle a_{I}(t)=a_{Q}(t)}$相同，bk(t) 为 +1，反之则为 -1。若${\displaystyle a_{I}(t)}$ 为 1， ${\displaystyle \phi _{k}}$ 则为零，反之则为 ${\displaystyle \pi }$。由此可见，信号是经频率及相位调制的， 而且相位作连续线性变化。

## 注释

1. ^ M.L Doelz and E.T. Heald, Minimum Shift Data Communication System, US Patent 2977417, 1958, http://www.freepatentsonline.com/2977417.html

## 参考文献

• Subbarayan Pasupathy, Minimum Shift Keying: A Spectrally Efficient Modulation, IEEE Communications Magazine, 1979
• R. de Buda, Fast FSK Signals and their Demodulation, Can. Elec. Eng. J. Vol. 1, Number 1, 1976.
• F. Amoroso, Pulse and Spectrum Manipulation in the Minimum (Frequency) Shift Keying (MSK) Format, IEEE Trans.
• Document from the University of Hull giving a thorough description of GMSK.