RESTORING BINARY SIGNAL FROM LOW FREQUENCIES

>>Is the function s(x) cyclostationary or not?
>>
>>If it is cyclostationary, then the task is the typical problem of the 
>>digital communication and there are many ways for solution depending on

>>L(x).
>>
>>If s(x) is not cyclostationary, then the problem is non-trivial and the

>>solution may not be unique.
>
>I don't see how cyclostationarity is relevant.  The OP did not say it
>comes from a random process.  In fact his example is rather
deterministic.

I understand a deterministic signal can also be cyclostationary; so never
mind that part. 

Still, I don't see why exactly one needs this condition.  Does anyone have
a good explanation?

Emre

On Oct 31, 6:44&#4294967295;pm, "emre" <egu...@ece.neu.edu> wrote:
> To the OP: there may be an extremely neat solution to your problem. &#4294967295;If
> you have enough Fourier domain measurements, you can reconstruct your
> signal *exactly* with an overwhelming probability, assuming the number of
> jumps and/or the nonzero values in your signal is &#4294967295;small (i.e. sparse) with
> respect to the total number of the samples. &#4294967295;See the below reference [1].
>
> Hope this helps,
>
> Emre
>
> [1] E. J. Cand&#4294967295;s, J. Romberg and T. Tao. Robust uncertainty principles:
> exact signal reconstruction from highly incomplete frequency information.
> IEEE Trans. Inform. Theory, 52 489-509.

Emre,

Perfect reference! Thank you very much. We can consider this thread to
be over.

Yuri