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- 주제어 : signals with finite rate of innovation (검색결과 1 건)
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Random sampling and reconstruction of signals with finite rate of innovation
Yingchun Jiang,Junjian Zhao 대한수학회 2022 대한수학회보 Vol.59 No.2
In this paper, we mainly study the random sampling and reconstruction of signals living in the subspace $V^p(\Phi,\Lambda)$ of $L^p(\mathbb{R}^d)$, which is generated by a family of molecules $\Phi$ located on a relatively separated subset $\Lambda\subset \mathbb{R}^d$. The space $V^p(\Phi,\Lambda)$ is used to model signals with finite rate of innovation, such as stream of pulses in GPS applications, cellular radio and ultra wide-band communication. The sampling set is independently and randomly drawn from a general probability distribution over $\mathbb{R}^d$. Under some proper conditions for the generators $\Phi=\{\phi_\lambda:\lambda\in \Lambda\}$ and the probability density function $\rho$, we first approximate $V^{p}(\Phi,\Lambda)$ by a finite dimensional subspace $V^{p}_N(\Phi,\Lambda)$ on any bounded domains. Then, we prove that the random sampling stability holds with high probability for all signals in $V^{p}(\Phi,\Lambda)$ whose energy concentrate on a cube when the sampling size is large enough. Finally, a reconstruction algorithm based on random samples is given for signals in $V^{p}_N(\Phi,\Lambda)$.
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