正交调制原理(未完)

1、原理:

调制信号的一般模型:

s(t)=m(t)*cos(2\pi f_{c}t+\varphi)

将其展开,有:

s(t)=m(t)*(cos(2\pi f_{c}t)cos(\varphi )-sin(2\pi f_{c}t)sin(\varphi ))

重新组合:

s(t)=m(t)cos(\varphi )*cos(2\pi f_{c}t)-m(t)sin(\varphi )*sin(2\pi f_{c}t)

又因为:

I(t)=m(t)cos(\varphi );Q(t)=m(t)sin(\varphi );

所以:

s(t)=I(t)cos(2\pi f_{c}t)-Q(t)sin(2\pi f_{c}t)

I、Q为极坐标系的表示方法。其中,I为同相(in-phase)载波幅度,Q为正交(quadrature-phase)载波幅度。

频谱反转:

s(t)=I(t)cos(2\pi f_{c}t)+Q(t)sin(2\pi f_{c}t)

2、调制和频谱搬移

已知信号的频谱:

F(w)=\int x(t)e^{-jwt}dt

调制则与载波相乘cos(w_{c}t)相乘,其频谱

F^{'}(w)=\int x(t)e^{-jwt}cos(w_{c}t)dt

F^{'}(w)=\frac{1}{2}F(w-w_{c})+\frac{1}{2}F(w+w_{c})

频谱搬移则与e^{jw_{c}t}相乘,其频谱

F^{''}(w)=\int x(t)e^{-jwt}e^{jw_{c}t}dt

F^{''}(w)=F(w-w_{c})

 

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转载自blog.csdn.net/kemi450/article/details/90712832