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Re: Want a smooth function from Arg[ ]


  • To: mathgroup@smc.vnet.net
  • Subject: [mg12519] Re: Want a smooth function from Arg[ ]
  • From: Mario Parra <parra@busco.lanl.gov>
  • Date: Sat, 23 May 1998 18:10:49 -0400
  • Organization: Los Alamos National Laboratory

Sean Ross wrote:

>  The method you gave works beautifully for continuous functions or for

> smooth, discrete data.  If there is the possibility of noise in the
> input function, then the problem becomes harder.  My own meeting of
> this problem occurs in Fourier propagation of light.  The phase output

> of an fft is totally chopped up for the same reason the Arg chops it
> up.  I have had some success in minimizing the numerical first and
> second derivatives, but it is far from a trivial problem, especially
in
> two dimensions.  If you hear of a different approach than an
> after-the-fact hunting for discontinuities, please let me know.

  Take a look the following papers:

    Phase unwrapping of signals propagated under the ....
        IEEE trans. on Acoustics, Speech and signal processing
        Vol 36, No 5. May 1988.

    Exact computation of the Unwrapped phase of a ....
          IEEE trans. on Acoustics, Speech and signal processing
        Vol 36, No 11. Nov 1988.

    A direct relation between a signal time series .....
          IEEE trans. on Acoustics, Speech and signal processing
        Vol ASSP-30, No 5. Oct 1982.

    Phase unwrapping of digital signals.
          IEEE trans. on Acoustics, Speech and signal processing
        Vol 37, No 11. Nov 89.

    A new phase unwrapping algorithm.
          IEEE trans. on Acoustics, Speech and signal processing
        Vol ASSP-25, No 2. Apr 77.

These papers address the problems that phase unwrapping gives. I recall
some of them talk about noise.... Hope they are helpful.

-Mario





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