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Given a complex-valued signal with a certain delay $s(t-\tau)$ for which we sample $N$ instants $$ \mathbf{s(\tau)}=\left[s(0-\tau),\ldots,s\left(\frac{N-1}{f_s}-\tau\right)\right]^T $$ at Nyquist rate $f_s\geq 2B$, and such signal is band-limited, i.e. $$ S(f)=FT\{s(t)\}=0 \quad\text{for} \quad |f| > B. $$ Is there any result that sheds some light on the approximate dimension of the following set?: $$ \mathcal{U}=\left\{\mathbf{s}(\tau):0\leq\tau\leq T\right\} $$ In other words, is $\mathcal{U}$ (approximately) a subspace of $\mathbb{C}^N$ no matter what is the signal $s(t)$? And if yes, what is the dimension?

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  • $\begingroup$ You might consider adding a top-level tag in order to increase the visibility of this question. $\endgroup$
    – Stefan Kohl ♦
    Commented Oct 15, 2015 at 20:19
  • $\begingroup$ Can you give an example of tag? $\endgroup$
    – mermeladeK
    Commented Oct 17, 2015 at 1:18
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    $\begingroup$ I am not familiar with the topic of your question, so I'm not sure -- maybe one (or some) of the following fit: ca.analysis-and-odes fa.functional-analysis na.numerical-analysis $\endgroup$
    – Stefan Kohl ♦
    Commented Oct 17, 2015 at 8:49

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