Papoulis gerchberg cadzow algorithm for extrapolation of b - bandlimited functions

Discussion in 'Programmer's Corner' started by Vanesa Magar, Apr 18, 2009.

  1. Vanesa Magar

    Thread Starter New Member

    Apr 18, 2009
    Dear all,
    I am new to this forum so hopefully my enquiry is relevant.
    I am trying to use Papoulis algorithm to extrapolate an arbitrary function. However, the algorithm supposedly works for bandlimited functions, so my first idea was to extract the sinusoidal components of the signal and extrapolate those components. I used the program pgsin from Matlab Central, which I adapted to extrapolate any function to arbitrary points. However, the problem I had was that the function decayed to zero at the boundaries, which is not what I expected to find. My second idea was then to interpolate my time series with a function that would be bandlimited. I used a formula I found in Papoulis' book which interpolates any function, f(t), by a bandlimited function f_i(t) of the form
    f_i(t)=sum_{n=-\infty}^{n=+\infty} f(nT) sin(sigma(t-nT))/(sigma(t-nT)),
    where T is an interval and sigma is pi/T
    I did the interpolation and it seems f_i agrees well in the mid third of the time series but as I approach the limits f_i oscillates more and more. I thought of extracting the mid third, for which f_i gives good results, and try to extrapolate f_i to the left and the right and see if these left and right extrapolations would be close to the signal I started with. Again this failed, again because pgsin assumes I will decay to zero at the ends, which is definitely not true.
    My question is: Has anyone tried to use Papoulis' algorithm to extrapolate arbitrary functions? and did it work? I am not sure whether I am not finding the answer because Papoulis will not work or because pgsin needs to be modified further. Can anyone give me some hints? Has anyone tried other alternatives? I have used AR models in the past with good results but I am trying to find an alternative that would improve my predictions.
    Thanks in advance!