Quadrature modulation principle (unfinished)

1, Principle:

General model modulated signal:

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

To expand, there are:

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

Regroup:

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

also because:

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

and so:

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

I, Q is a polar coordinate system representation. Wherein, I is the in-phase (in-phase) carrier amplitude, Q is an orthogonal (quadrature-phase) carrier amplitude.

Spectrum inversion:

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

2, the modulation and spectrum shifting

Known signal spectrum:

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

Is multiplied by the modulated carrier cos(w_{c}t)is multiplied by its spectrum

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})

Spectrum shifting and then e^{jw_{c}t}multiplied by its spectrum

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

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

 

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Origin blog.csdn.net/kemi450/article/details/90712832