Phase recover

Phase recover

Post by Simba L » Sat, 08 Nov 2003 05:10:48

  I am dealing with a phase recover& unwrap problem.
  Suppose there is a temp*signal which is given by:        
          I = Ib + Im*cos(phi(t) + phi0);
  where Ib, Im and phi0 is constant or with quite lower frequency comparing
  with the phase signal: phi(t). Of coz 't' means time.
  My problem is how to recover the 'phi(t)' signal.

  This problem is simple if
          phi(t) = omega*t;
  The simplest way is utilizing Hilbert Tranform I guess.
  But the signal I got is sth like:
          phi(t) = omega * cos(k*t);
  Frequency of the signal 'I' is then quite complicated. I have tried
  Hilbert Transform and no wonder I failed.

  Can anyone give some idea?

  I appreciate for any advice.


Phase recover

Post by Ohad Ga » Sat, 08 Nov 2003 08:25:24


under the condition, that your data is sampled dense enough (i.e. k
<< 1/T), you could try a strait forward method.

your function is:
I = A + B*cos( w*cos(k*t) + phi0 )

lets define:

U = (I-A)/B = cos( w*cos(k*t) + phi0 )

where A and B are found by (approximately):
B = max(I)-min(I)
A = ( max(I)+min(I) )/2

then find:

V = acos(U) = w*cos(k*t) + phi0

assuming that w and phi0 are constants as well, find them like you
found A and B.

W = (V-phi0)/w

and last,

R = fft(W) -> the peaks will indicate the value of "k" (you know
the Fourier theory)

if the noise is fairly low, and A,B,phi0,w are approximately
constants, this should work.



1. Bandpass with zero phase shift or constant phase shift within passband?


I am running simulation that requires a bandpass filter that has zero or
constant phase shift within the passband. Is it possible designa such a filter?
There is a filtfilt function in Matlab but it is not suitable for simulation
type of a problem. If possible, please email directly to me (I don't read
this group very often).

Thanks in advance.

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