finding phase shift using i and q signals

Discussion in 'Math' started by ashwini1, Aug 1, 2009.

  1. ashwini1

    Thread Starter New Member

    Aug 1, 2009
    9
    0
    Hi,

    I have read in one document that the phase of a signal (say sine wave) can be calculated by making use of I and Q signals of it. For ex:
    Fs = 10e3;
    t=(0:Fs)/Fs';
    ph=45;
    x=sin(2*pi*50*t+(ph*pi/180));

    i=x.*cos(2*pi*50*t);
    q=x.*sin(2*pi*50*t);

    it was mentioned that by subtracting the max values of i and q, i will get the ph value.

    But that is not happening.

    what is wrong with this ??
    i have to make use of i and q signals to find the ph.

    Can anyone help me plz..

    Ashwini :)
     
  2. rspuzio

    Active Member

    Jan 19, 2009
    77
    0
    Apply the angle addition formula to your expression:

     x = \sin (2 \pi 50 t+ (\phi \pi/180)) =<br />
\sin (2 \pi 50 t) \cos (\phi \pi/180)  +<br />
\cos (2 \pi 50 t) \sin (\phi \pi/180)<br />

    Now that you have x expressed as a superposition of
     \sin (2 \pi 50 t) and
      \cos (2 \pi 50 t) , it should be easy enough
    to multiply by a sine or cosine and find the maximum.
     
  3. rspuzio

    Active Member

    Jan 19, 2009
    77
    0
    You can also use the trigonometric identities for
    product of two sines or a product of a sine and
    a cosine:

    i=\sin(2 \pi 50 t+(\phi \pi/180)) \cos(2 \pi 50 t) =<br />
{1 \over 2} \left[  \sin (\phi \pi/180) + <br />
\sin (4 \pi 50 t+(\phi \pi/180))  \right]
    q=\sin(2 \pi 50 t+(\phi \pi/180)) \sin(2 \pi 50 t) = <br />
{1 \over 2} \left[  \cos (\phi \pi/180) + <br />
\cos (4 \pi 50 t+(\phi \pi/180))  \right]

    Note that in these expressions the first term is constant
    whilst the second term is a sine or a cosine so that its
    maximum value will be 1. So we have that the
    maximum value of i is

     i_{\rm max} =  {1 \over 2} \left[  \sin (\phi \pi/180) <br />
+ 1 \right]

    and the maximum value for q is

     q_{\rm max} =  {1 \over 2} \left[  \cos (\phi \pi/180)<br />
+ 1 \right]

    So we see that the maximum values of i and q depend
    on  \phi . To recover the value of  \phi
    we can use inverse trig functions. Not quite as simple as
    subtracting them, but you can use the maximum values
    of i and q to determine the phase.
     
  4. ashwini1

    Thread Starter New Member

    Aug 1, 2009
    9
    0
    Thank you very much ..
    It helped me a lot ..
    I got the required output. :)
     
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