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In-phase component and Quadrature component

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banh

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x[n] = Acos(ωn + Φ)= AcosΦcosωn-AsinΦsinωn = xi[n]+xq[n]

xi[n] is called in-phase component
while xq[n] quadrature component

what are the meanings and significance of these terms?


btw, can this forum transform latex math into picture to display?
 

hi,
basically you are trying to decompose a signal into a vector space having basis function as cos and sin which are orthogonal to each other.
It is like having a co-ordinate system
say you have defined two axes as x and y and any point in it can be specidied in terms of x-component as well as y component it is similar to this analogy.
pimr
 

u(t)=A(t)cos(ω0*t+θ)
AM modulation -change A(t) , θ=const
FM,ΦM - change Θ, A(t)=const
If you need some advanced modulation techniques, you will have to change both amplitude and phase. Standard analyzis with polar Amplitude and angle is not so suitable.
It is much easier to analyze signal by decomposing it into I/Q components (rectangular projections of polar plot).
You can make I/Q components modulating it with cos and sin wave.
On this are based digital modulation techniques.


Acosθcosω0-Asinθsinω0 = I*cosw0-Q*sinw0
I=Acosθ inphase
Q=Asinθ quadrature
 

x(t) = Real{[I(t)+j*Q(t)]*exp(j*w0*t)}

Any passband signal with carrier w0 can be expressed in this form, as the product of a complex baseband signal (I+j*Q) by the complex carrier exp(j*w0*t). The result is modulated both in amplitude and phase
These (I and Q) are the in-phase and quadrature components.
The representation of [I(t)+j*Q(t)] in the cartesian plane is the vectorial form of the complex signal.
Regards

Z
 

In agilent AN1298 application note is good explained, physical meaning of OI and Q components.
 

You can fount it on
**broken link removed**
 

Hi,
the simple explanation is,
Sine and Cosine are orthogonal and this means if we decompose a signal into sine and cosine parts you have basically created two signals that are distinguishable over the same bandwidth. This principle is used in quadrature modulation and in removing the orthogonal noise components.
B R
Madhukar
 

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