Multirate asynchronous sampling of sparse multiband signals

source: © 2008 Optical Society of America

Because optical systems have a huge bandwidth and are capable of generating low-noise short pulses, they are ideal for undersampling multiband signals that are located within a very broad frequency range. We propose a new scheme for reconstructing multiband signals that occupy a small part of a given broad frequency range under the constraint of a small number of sampling channels. The scheme, which we call multirate sampling (MRS), entails gathering samples at several different rates whose sum is significantly lower than the Nyquist sampling rate. The number of channels does not depend on any characteristics of a signal. In order to be implemented with simplified hardware, the reconstruction method does not rely on the synchronization between different sampling channels. Also, because the method does not solve a system of linear equations, it avoids one source of lack of robustness of previously published undersampling schemes. Our simulations indicate that our MRS scheme is robust both to different signal types and to relatively high noise levels. The scheme can be implemented easily with optical sampling systems.  [Read more…]

Fig. 2 Illustration demonstrating how support consistency is checked. The input of the algorithm is the sampled signals whose spectra 𝑋1(𝑓) and 𝑋2(𝑓) are shown Figs. 1b, 1c, respectively; their respective indicator functions ℐ1(𝑓) and ℐ2(𝑓) are shown in Figs. 2a, 2b. Figure 2c shows the indicator function ℐ(𝑓)=ℐ1(𝑓)ℐ2(𝑓) . In Figs. 2d, 2e, we check whether the subset 𝒰={𝑈2}∊𝒫{𝑈} is support consistent. Figures 2d, 2e show the indicator functions for the downconversion of 𝑈2 at rates 𝐹1 and 𝐹2:ℐ1𝑈2(𝑓) and ℐ2𝑈2(𝑓) , respectively. The dashed lines illustrate 𝑈2 , −U2 , and their downconversions. It is evident that the functions ℐ1(𝑓) and ℐ1𝑈2(𝑓) are not equal. Hence, 𝒰={𝑈2} is not a support-consistent combination.

Amir Rosenthal, Alex Linden, and Moshe Horowitz, “Multirate asynchronous sampling of sparse multiband signals,” J. Opt. Soc. Am. A 25, 2320-2330 (2008)