Abstract:
Filtering of multi-band bandlimited signals by means of a linear digital filter with one or more stopbands is explored. The main goal of the paper is to demonstrate that such a task can be accomplished using sampling rates lower than Landau rate, where the Landau rate is defined as the total bandwidth of the input signal. In order to reach such low rates Periodic Nonuniform Sampling is employed. We show that the proposed filtering method is most efficient when bandpass and multiband filtering is required. Necessary and sufficient conditions for filtering are derived, and an algorithm for designing PNS grids that allow sub-Landau sampling and filtering is proposed. Reconstruction systems are discussed and experimental examples are presented, which confirm the feasibility of the approach.

Abstract:
We demonstrate experimentally an optical system for under-sampling several bandwidth limited signals with carrier frequencies that are not known apriori that can be located anywhere within a very broad frequency region between 0-18 GHz. The system is based on under-sampling asynchronously at three different sampling rates. The pulses required for the under-sampling are generated by a combination of an electrical comb generator and an electro-absorption modulator. To reduce loss and improve performance the implementation of the optical system is based on a wavelength division multiplexing technique. An accurate reconstruction of both the phase and the amplitude of the signals was obtained when two chirped signals generated simultaneously were sampled.

Abstract:
This paper presents a regularized sampling method for multiband signals, that makes it possible to approach the Landau limit, while keeping the sensitivity to noise at a low level. The method is based on band-limited windowing, followed by trigonometric approximation in consecutive time intervals. The key point is that the trigonometric approximation "inherits" the multiband property, that is, its coefficients are formed by bursts of non-zero elements corresponding to the multiband components. It is shown that this method can be well combined with the recently proposed synchronous multi-rate sampling (SMRS) scheme, given that the resulting linear system is sparse and formed by ones and zeroes. The proposed method allows one to trade sampling efficiency for noise sensitivity, and is specially well suited for bounded signals with unbounded energy like those in communications, navigation, audio systems, etc. Besides, it is also applicable to finite energy signals and periodic band-limited signals (trigonometric polynomials). The paper includes a subspace method for blindly estimating the support of the multiband signal as well as its components, and the results are validated through several numerical examples.

Abstract:
The reconstruction of an unknown continuously defined function from the samples of the responses of linear time-invariant (LTI) systems sampled by the th Nyquist rate is the aim of the generalized sampling. Papoulis (1977) provided an elegant solution for the case where is a band-limited function with finite energy and the sampling rate is equal to times cutoff frequency. In this paper, the scope of the Papoulis theory is extended to the case of bandpass signals. In the first part, a generalized sampling theorem (GST) for bandpass signals is presented. The second part deals with utilizing this theorem for signal recovery from nonuniform samples, and an efficient way of computing images of reconstructing functions for signal recovery is discussed.

Abstract:
Periodic nonuniform sampling is a known method to sample spectrally sparse signals below the Nyquist rate. This strategy relies on the implicit assumption that the individual samplers are exposed to the entire frequency range. This assumption becomes impractical for wideband sparse signals. The current paper proposes an alternative sampling stage that does not require a full-band front end. Instead, signals are captured with an analog front end that consists of a bank of multipliers and lowpass filters whose cutoff is much lower than the Nyquist rate. The problem of recovering the original signal from the low-rate samples can be studied within the framework of compressive sampling. An appropriate parameter selection ensures that the samples uniquely determine the analog input. Moreover, the analog input can be stably reconstructed with digital algorithms. Numerical experiments support the theoretical analysis.

Abstract:
This paper discussed the uniform under-sampling of multiple bandpass signals in digital receiver. For these multiple real or complex bandpass signals having arbitrary band position and bandwidth, the acceptable sampling rate has been given. Using this sampling rate to sample the input bandpass signal, an efficient data compression can be gotten. In the same time using band pass filter, these multiple bandpass signals can be transferred to the lower frequency. Finally, an example is given to show the correctness of the uniform sampling method of multiple bandpass signals.

Abstract:
In many applications of current interest, the observations are represented as a signal defined over a graph. The analysis of such signals requires the extension of standard signal processing tools. Building on the recently introduced Graph Fourier Transform, the first contribution of this paper is to provide an uncertainty principle for signals on graph. As a by-product of this theory, we show how to build a dictionary of maximally concentrated signals on vertex/frequency domains. Then, we establish a direct relation between uncertainty principle and sampling, which forms the basis for a sampling theorem for graph signals. Since samples location plays a key role in the performance of signal recovery algorithms, we suggest and compare a few alternative sampling strategies. Finally, we provide the conditions for perfect recovery of a useful signal corrupted by sparse noise, showing that this problem is also intrinsically related to vertex-frequency localization properties.

Abstract:
In this work, we analyze modulated sampling schemes, such as the Nyquist Folding Receiver, which are highly efficient, readily implementable, non-uniform sampling schemes that allows for the blind estimation of a narrow-band signal's spectral content and location in a wide-band environment. This non-uniform sampling, achieved by narrow-band modulation of the RF instantaneous sample rate, results in a frequency domain point spread function that is between the extremes obtained by uniform sampling and totally random sampling. As a result, while still preserving structured aliasing, the modulated sampling scheme is also useful in a compressive sensing (CS) setting. We estimate restricted isometry property (RIP) constants for CS matrices induced by such modulated sampling schemes and use those estimates to determine the amount of sparsity needed for signal recovery. This is followed by a demonstration and analysis of Orthogonal Matching Pursuit's ability to reconstruct signals from noisy non-uniform samples.

Abstract:
We study the problem of sampling k-bandlimited signals on graphs. We propose two sampling strategies that consist in selecting a small subset of nodes at random. The first strategy is non-adaptive, i.e., independent of the graph structure, and its performance depends on a parameter called the graph coherence. On the contrary, the second strategy is adaptive but yields optimal results. Indeed, no more than O(k log(k)) measurements are sufficient to ensure an accurate and stable recovery of all k-bandlimited signals. This second strategy is based on a careful choice of the sampling distribution, which can be estimated quickly. Then, we propose a computationally efficient decoder to reconstruct k-bandlimited signals from their samples. We prove that it yields accurate reconstructions and that it is also stable to noise. Finally, we conduct several experiments to test these techniques.

Abstract:
Bandpass time-continuos signals are shown being able to be uniquely expressed in terms of the samples gi(nTv) of the impulse responses gi(t) of m linear time-invariant systems with input f(t) sampled at 1/m Nyquist rate. Various known extensions of the sampling theorem can be regarded as special cases of the resulting generalized sampling expansion of f(t).