Compressive and Noncompressive Power Spectral Density Estimation from Periodic Nonuniform Samples

This paper presents a novel power spectral density estimation technique for band-limited, wide-sense stationary signals from sub-Nyquist sampled data. The technique employs multi-coset sampling and incorporates the advantages of compressed sensing (CS) when the power spectrum is sparse, but applies to sparse and nonsparse power spectra alike. The estimates are consistent piecewise constant approximations whose resolutions (width of the piecewise constant segments) are controlled by the periodicity of the multi-coset sampling. We show that compressive estimates exhibit better tradeoffs among the estimator's resolution, system complexity, and average sampling rate compared to their noncompressive counterparts. For suitable sampling patterns, noncompressive estimates are obtained as least squares solutions. Because of the non-negativity of power spectra, compressive estimates can be computed by seeking non-negative least squares solutions (provided appropriate sampling patterns exist) instead of using standard CS recovery algorithms. This flexibility suggests a reduction in computational overhead for systems estimating both sparse and nonsparse power spectra because one algorithm can be used to compute both compressive and noncompressive estimates.Comment: 26 pages, single spaced, 9 figure

From Theory to Practice: Sub-Nyquist Sampling of Sparse Wideband Analog Signals

Conventional sub-Nyquist sampling methods for analog signals exploit prior information about the spectral support. In this paper, we consider the challenging problem of blind sub-Nyquist sampling of multiband signals, whose unknown frequency support occupies only a small portion of a wide spectrum. Our primary design goals are efficient hardware implementation and low computational load on the supporting digital processing. We propose a system, named the modulated wideband converter, which first multiplies the analog signal by a bank of periodic waveforms. The product is then lowpass filtered and sampled uniformly at a low rate, which is orders of magnitude smaller than Nyquist. Perfect recovery from the proposed samples is achieved under certain necessary and sufficient conditions. We also develop a digital architecture, which allows either reconstruction of the analog input, or processing of any band of interest at a low rate, that is, without interpolating to the high Nyquist rate. Numerical simulations demonstrate many engineering aspects: robustness to noise and mismodeling, potential hardware simplifications, realtime performance for signals with time-varying support and stability to quantization effects. We compare our system with two previous approaches: periodic nonuniform sampling, which is bandwidth limited by existing hardware devices, and the random demodulator, which is restricted to discrete multitone signals and has a high computational load. In the broader context of Nyquist sampling, our scheme has the potential to break through the bandwidth barrier of state-of-the-art analog conversion technologies such as interleaved converters.Comment: 17 pages, 12 figures, to appear in IEEE Journal of Selected Topics in Signal Processing, the special issue on Compressed Sensin

Assessment of sub-Nyquist deterministic and random data sampling techniques for operational modal analysis

This paper assesses numerically the potential of two different spectral estimation approaches supporting non-uniform in time data sampling at sub-Nyquist average rates (i.e., below the Nyquist frequency) to reduce data transmission payloads in wireless sensor networks (WSNs) for operational modal analysis (OMA) of civil engineering structures. This consideration relaxes transmission bandwidth constraints in WSNs and prolongs sensor battery life since wireless transmission is the most energy-hungry on-sensor operation. Both the approaches assume acquisition of sub-Nyquist structural response acceleration measurements and transmission to a base station without on-sensor processing. The response acceleration power spectral density matrix is estimated directly from the sub-Nyquist measurements and structural mode shapes are extracted using the frequency domain decomposition algorithm. The first approach relies on the compressive sensing (CS) theory to treat sub-Nyquist randomly sampled data assuming that the acceleration signals are sparse/compressible in the frequency domain (i.e., have a small number of Fourier coefficients with significant magnitude). The second approach is based on a power spectrum blind sampling (PSBS) technique considering periodic deterministic sub-Nyquist “multi-coset” sampling and treating the acceleration signals as wide-sense stationary stochastic processes without posing any sparsity conditions. The modal assurance criterion (MAC) is adopted to quantify the quality of mode shapes derived by the two approaches at different sub-Nyquist compression rates (CRs) using computer-generated signals of different sparsity and field-recorded stationary data pertaining to an overpass in Zurich, Switzerland. It is shown that for a given CR, the performance of the CS-based approach is detrimentally affected by signal sparsity, while the PSBS-based approach achieves MAC>0.96 independently of signal sparsity for CRs as low as 11% the Nyquist rate. It is concluded that the PSBS-based approach reduces effectively data transmission requirements in WSNs for OMA, without being limited by signal sparsity and without requiring a priori assumptions or knowledge of signal sparsity

Compressive power spectrum sensing for vibration-based output-only system identification of structural systems in the presence of noise

Motivated by the need to reduce monetary and energy consumption costs of wireless sensor networks in undertaking output-only/operational modal analysis of engineering structures, this paper considers a multi-coset analog-toinformation converter for structural system identification from acceleration response signals of white noise excited linear damped structures sampled at sub-Nyquist rates. The underlying natural frequencies, peak gains in the frequency domain, and critical damping ratios of the vibrating structures are estimated directly from the sub-Nyquist measurements and, therefore, the computationally demanding signal reconstruction step is by-passed. This is accomplished by first employing a power spectrum blind sampling (PSBS) technique for multi-band wide sense stationary stochastic processes in conjunction with deterministic non-uniform multi-coset sampling patterns derived from solving a weighted least square optimization problem. Next, modal properties are derived by the standard frequency domain peak picking algorithm. Special attention is focused on assessing the potential of the adopted PSBS technique, which poses no sparsity requirements to the sensed signals, to derive accurate estimates of modal structural system properties from noisy sub- Nyquist measurements. To this aim, sub-Nyquist sampled acceleration response signals corrupted by various levels of additive white noise pertaining to a benchmark space truss structure with closely spaced natural frequencies are obtained within an efficient Monte Carlo simulation-based framework. Accurate estimates of natural frequencies and reasonable estimates of local peak spectral ordinates and critical damping ratios are derived from measurements sampled at about 70% below the Nyquist rate and for SNR as low as 0db demonstrating that the adopted approach enjoys noise immunity

Advancements of MultiRate Signal processing for Wireless Communication Networks: Current State Of the Art

With the hasty growth of internet contact and voice and information centric communications, many contact technologies have been urbanized to meet the stringent insist of high speed information transmission and viaduct the wide bandwidth gap among ever-increasing high-data-rate core system and bandwidth-hungry end-user complex. To make efficient consumption of the limited bandwidth of obtainable access routes and cope with the difficult channel environment, several standards have been projected for a variety of broadband access scheme over different access situation (twisted pairs, coaxial cables, optical fibers, and unchanging or mobile wireless admittance). These access situations may create dissimilar channel impairments and utter unique sets of signal dispensation algorithms and techniques to combat precise impairments. In the intended and implementation sphere of those systems, many research issues arise. In this paper we present advancements of multi-rate indication processing methodologies that are aggravated by this design trend. The thesis covers the contemporary confirmation of the current literature on intrusion suppression using multi-rate indication in wireless communiquE9; networks

Compressive Source Separation: Theory and Methods for Hyperspectral Imaging

With the development of numbers of high resolution data acquisition systems and the global requirement to lower the energy consumption, the development of efficient sensing techniques becomes critical. Recently, Compressed Sampling (CS) techniques, which exploit the sparsity of signals, have allowed to reconstruct signal and images with less measurements than the traditional Nyquist sensing approach. However, multichannel signals like Hyperspectral images (HSI) have additional structures, like inter-channel correlations, that are not taken into account in the classical CS scheme. In this paper we exploit the linear mixture of sources model, that is the assumption that the multichannel signal is composed of a linear combination of sources, each of them having its own spectral signature, and propose new sampling schemes exploiting this model to considerably decrease the number of measurements needed for the acquisition and source separation. Moreover, we give theoretical lower bounds on the number of measurements required to perform reconstruction of both the multichannel signal and its sources. We also proposed optimization algorithms and extensive experimentation on our target application which is HSI, and show that our approach recovers HSI with far less measurements and computational effort than traditional CS approaches.Comment: 32 page

Compressive techniques for sub-Nyquist data acquisition & processing in vibration-based structural health monitoring of engineering structures

Vibration-based structural health monitoring (VSHM) is an automated method for assessing the integrity and performance of dynamically excited structures through processing of structural vibration response signals acquired by arrays of sensors. From a technological viewpoint, wireless sensor networks (WSNs) offer less obtrusive, more economical, and rapid VSHM deployments in civil structures compared to their tethered counterparts, especially in monitoring large-scale and geometrically complex structures. However, WSNs are constrained by certain practical issues related to local power supply at sensors and restrictions to the amount of wirelessly transmitted data due to increased power consumptions and bandwidth limitations in wireless communications. The primary objective of this thesis is to resolve the above issues by considering sub-Nyquist data acquisition and processing techniques that involve simultaneous signal acquisition and compression before transmission. This drastically reduces the sampling and transmission requirements leading to reduced power consumptions up to 85-90% compared to conventional approaches at Nyquist rate. Within this context, the current state-of-the-art VSHM approaches exploits the theory of compressive sensing (CS) to acquire structural responses at non-uniform random sub-Nyquist sampling schemes. By exploiting the sparse structure of the analysed signals in a known vector basis (i.e., non-zero signal coefficients), the original time-domain signals are reconstructed at the uniform Nyquist grid by solving an underdetermined optimisation problem subject to signal sparsity constraints. However, the CS sparse recovery is a computationally intensive problem that strongly depends on and is limited by the sparsity attributes of the measured signals on a pre-defined expansion basis. This sparsity information, though, is unknown in real-time VSHM deployments while it is adversely affected by noisy environments encountered in practice. To efficiently address the above limitations encountered in CS-based VSHM methods, this research study proposes three alternative approaches for energy-efficient VSHM using compressed structural response signals under ambient vibrations. The first approach aims to enhance the sparsity information of vibrating structural responses by considering their representation on the wavelet transform domain using various oscillatory functions with different frequency domain attributes. In this respect, a novel data-driven damage detection algorithm is developed herein, emerged as a fusion of the CS framework with the Relative Wavelet Entropy (RWE) damage index. By processing sparse signal coefficients on the harmonic wavelet transform for two comparative structural states (i.e., damage versus healthy state), CS-based RWE damage indices are retrieved from a significantly reduced number of wavelet coefficients without reconstructing structural responses in time-domain. The second approach involves a novel signal-agnostic sub-Nyquist spectral estimation method free from sparsity constraints, which is proposed herein as a viable alternative for power-efficient WSNs in VSHM applications. The developed method relies on Power Spectrum Blind Sampling (PSBS) techniques together with a deterministic multi-coset sampling pattern, capable to acquire stationary structural responses at sub-Nyquist rates without imposing sparsity conditions. Based on a network of wireless sensors operating on the same sampling pattern, auto/cross power-spectral density estimates are computed directly from compressed data by solving an overdetermined optimisation problem; thus, by-passing the computationally intensive signal reconstruction operations in time-domain. This innovative approach can be fused with standard operational modal analysis algorithms to estimate the inherent resonant frequencies and modal deflected shapes of structures under low-amplitude ambient vibrations with the minimum power, computational and memory requirements at the sensor, while outperforming pertinent CS-based approaches. Based on the extracted modal in formation, numerous data-driven damage detection strategies can be further employed to evaluate the condition of the monitored structures. The third approach of this thesis proposes a noise-immune damage detection method capable to capture small shifts in structural natural frequencies before and after a seismic event of low intensity using compressed acceleration data contaminated with broadband noise. This novel approach relies on a recently established sub-Nyquist pseudo-spectral estimation method which combines the deterministic co-prime sub-Nyquist sampling technique with the multiple signal classification (MUSIC) pseudo-spectrum estimator. This is also a signal-agnostic and signal reconstruction-free method that treats structural response signals as wide-sense stationary stochastic processes to retrieve, with very high resolution, auto-power spectral densities and structural natural frequency estimates directly from compressed data while filtering out additive broadband noise