Potential Applications In Signal Processing Research Articles

Duality for matrix-valued wave packet frames in L2(ℝd, ℂs×r)

Dual frames are generalized Riesz bases which have potential applications in signal processing. In this paper, the construction of dual frames of matrix-valued wave packet systems in the matrix-valued function space [Formula: see text] from dual pairs of atomic wave packet frames in [Formula: see text] is studied. A class of matrix-valued dual generators from its associated dual pair of atomic wave packets has been obtained. We provide a characterization of matrix-valued dual window functions in terms of orthogonality of wave packet Bessel sequences. A perturbation result with respect to window functions for matrix-valued dual frames is given. It is well known that an orthogonal Parseval Hilbert frame for a Hilbert space turned out be an orthonormal basis for the space, however, this is not true for an orthogonal matrix-valued wave packet Parseval frame for the underlying matrix-valued function space. We give a type of matrix-valued orthonormal basis associated with an orthonormal basis of [Formula: see text].

Absorption of magnons in dispersively coupled hybrid quantum systems

Phenomena involved in magnons have attracted extensive attention for several decades because of their challenging physical properties, powerful capabilities, and potential applications in signal processing in the microwave frequency range. In this work study we study the steady-state dynamic processes of a hybrid quantum system based on magnonics, where the magnon mode couples dispersively to a superconducting qubit. We find that the dispersive coupling between the qubit and magnons causes the system to be bistable and we discuss in detail an interesting phenomenon of dispersive-coupling-induced absorption of magnons. Furthermore, a feasible scheme to measure the qubit-magnon dispersive shift by employing the absorption curves of the probe field is proposed. The results presented here are of great significance to the investigation of the steady-state dynamic behaviors of quantum magnonics in a strong-dispersive regime and may provide a theoretical reference for the realization of quantum sensing of magnons.

Mn(II) Ions Assisted Near-Infrared Single-Mode Lasing from an Individual Mn-Doped CdS Nanobelts

Tunable single-mode lasers are attractive for their potential applications in signal processing, optical communication, and displays. Here we present the Mn(II) ions assisted single-mode lasing occurring at near-infrared (NIR) band instead of the green emission band of CdS nanobelts (NBs) for the first time. Successful substation of Mn(II) ions at the tetrahedral Cd2+ cites in the CdS matrix were confirmed by EPR. Light Mn(II) doping (≤1%) in CdS belts not only red-shifted the Raman modes but also increased crystallinity compared to pure CdS NBs due to strong excitons-phonon couplings. Up to 3 µJ · cm-2 pumping fluence of ns laser, lightly doped CdS:Mn NBs show two photoluminescence (PL) emissions. First emission centered at 514.2 nm (green) corresponds to band-edge of CdS and an in-gap emission centered at 771.4 nm (NIR) corresponds to Mn(II) ions aggregates. After using intense excitation pulse, these NBs exhibited lasing at 791.4 nm with the lowest laser thresholds at 4.2 µJ · cm-2 in the CdS system. This lasing action is further confirmed by lifetime kinetics. The results indicated that the lasing in these NBs involves the localised excitons magnetic polarons and Farby-Perot (F-P) optical resonant processes at room temperature.

Vector-valued weak Gabor dual frames on discrete periodic sets

The notion of weak dual frames is a generalization of that of dual frames. Gabor analysis on discrete periodic sets has potential applications in signal processing. This paper addresses vector-valued weak Gabor dual frames on discrete periodic sets. We introduce the notions of its weak oblique Gabor dual, weak Gabor duals of types I and II for a Gabor system on a discrete periodic set. Using the Zak-transform matrix method, we characterize these three kinds of weak duals and their uniqueness. Finally, we give an explicit expression of a class of weak Gabor duals and provide some examples.

Vector-valued (super) weaving frames

Two frames {ϕi}i∈I and{ψi}i∈I for a separable Hilbert space H are woven if there are positive constants A≤B such that for every subset σ⊂I, the family {ϕi}i∈σ∪{ψi}i∈σc is a frame for H with frame bounds A,B. Bemrose et al. introduced weaving frames in separable Hilbert spaces and observed that weaving frames have potential applications in signal processing. Motivated by this, and the recent work of Balan in the direction of application of vector-valued frames (or superframes) in signal processing, we study vector-valued weaving frames. In this paper, first we give some fundamental properties of vector-valued weaving frames. It is shown that if a family of vector-valued frames is woven, then the corresponding family of frames for atomic spaces is woven, but the converse is not true. We present a technique for the construction of vector-valued woven frames from given woven frames for atomic spaces . Necessary and sufficient conditions for vector-valued weaving Riesz sequences are given. Several numerical examples are given to illustrate the results.

On the subdifferential of symmetric convex functions of the spectrum for symmetric and orthogonally decomposable tensors

The subdifferential of convex functions of the singular spectrum of real matrices has been widely studied in matrix analysis, optimization and automatic control theory. Convex optimization over spaces of tensors is now gaining much interest due to its potential applications in signal processing, statistics and engineering. The goal of this paper is to present an extension of the approach by Lewis [16] for the analysis of the subdifferential of certain convex functions of the spectrum of symmetric tensors. We give a complete characterization of the subdifferential of Schatten-type tensor norms for symmetric tensors. Some partial results in this direction are also given for Orthogonally Decomposable tensors.

Compressive Sensing Algorithms for Signal Processing Applications: A Survey

In digital signal processing (DSP), Nyquistrate sampling completely describes a signal by exploiting its bandlimitedness. Compressed Sensing (CS), also known as compressive sampling, is a DSP technique efficiently acquiring and reconstructing a signal completely from reduced number of measurements, by exploiting its compressibility. The measurements are not point samples but more general linear functions of the signal. CS can capture and represent sparse signals at a rate significantly lower than ordinarily used in the Shannon’s sampling theorem. It is interesting to notice that most signals in reality are sparse; especially when they are represented in some domain (such as the wavelet domain) where many coefficients are close to or equal to zero. A signal is called K-sparse, if it can be exactly represented by a basis, , and a set of coefficients , where only K coefficients are nonzero. A signal is called approximately K-sparse, if it can be represented up to a certain accuracy using K non-zero coefficients. As an example, a K-sparse signal is the class of signals that are the sum of K sinusoids chosen from the N harmonics of the observed time interval. Taking the DFT of any such signal would render only K non-zero values . An example of approximately sparse signals is when the coefficients , sorted by magnitude, decrease following a power law. In this case the sparse approximation constructed by choosing the K largest coefficients is guaranteed to have an approximation error that decreases with the same power law as the coefficients. The main limitation of CS-based systems is that they are employing iterative algorithms to recover the signal. The sealgorithms are slow and the hardware solution has become crucial for higher performance and speed. This technique enables fewer data samples than traditionally required when capturing a signal with relatively high bandwidth, but a low information rate. As a main feature of CS, efficient algorithms such as -minimization can be used for recovery. This paper gives a survey of both theoretical and numerical aspects of compressive sensing technique and its applications. The theory of CS has many potential applications in signal processing, wireless communication, cognitive radio and medical imaging.

ELECTROMAGNETICALLY INDUCED ABSORPTION IN METAMATERIALS IN THE INFRARED FREQUENCY

In this paper, the author studies, through numerical simulation, the classical analog of the electromagnetically induced absorption/re∞ection (EIA) in a planar metamaterial structure in the near infrared spectral region. The structure is designed by transforming an electromagnetically induced transparency (EIT) structure into an EIA structure using Babinet's principle. The structure exhibits a coupling between a bright mode (a complementary ring resonator (CRR)) and a dark mode (pair of parallel straight slits) imprinted on a glass substrate. A narrow absorption window, induced in a wide transparent window, is achieved by the structure and the strength of coupling is tuned by the degree of breaking symmetry and relative displacement of the two mode elements. Electromagnetically induced transparency (EIT) is a quantum mechanical phenomenon in which an absorption is transformed into a transparency, and this is associated with strong dispersion that reduces the group velocity (1{3). This phenomena has many potential applications in signal processing, optical flltering and sensing technologies (4{7). The classical analog of the EIT has been achieved and reported by many researchers using a planar metamaterial structures that are generally composed of two metallic elements imprinted on a dielectric substrate. The two elements are metallic resonators that act either as two bright modes or a bright and dark mode. A bright mode element couples strongly with the incident excitation fleld while the dark element does not couple with the incident fleld but couples with the magnetic fleld induced by the bright element. Several EIT metamaterial structures have been employed and reported in the microwave, terahertz and optical frequency regions (8{14). In this paper, we propose a new EIT structure that achieves a more pronounced narrow transparency window sandwiched between two absorption bands compared with a similar structure proposed in (14). Also compared with (14), the structure proposed here is independent of the polarization orientation with respect to the bright mode element. Then we transform this structure into an EIA structure using Babinet's principle (15,16), where a narrow absorption/re∞ection window is sandwiched between two transparency bands. The structures proposed here may be used as obscurant particles that allow the passage of a speciflc window/windows of the electromagnetic spectrum and obscure the neighboring frequencies, for this reason the transmission spectrum will be discussed and addressed for the potential obscurant applications. Although the orientational average response of the structure is what matters, it is of good beneflt to get the behavior in a given orientation. The EIT structure is composed of a metallic ring resonator (RR) which acts as a bright mode and a pair of metallic rods that act as a dark mode. Here we overlap the RR wide antenna resonance and the narrow line width quadrupole rod resonance, which in turn produces the EIT-like efiect. The structure is transformed into an EIA structure by replacing the metallic RR and the pair of rods resonator with complementary ring resonator (CRR) and

A nanoelectromechanical systems optical switch driven by optical gradient force

A nanoelectromechanical systems (NEMS) optical switch driven by optical gradient force is demonstrated. The switch consists of a free-standing ring resonator and two bus waveguides. When the free-standing ring is bended by the optical gradient force, the output transmission signal is tuned from the on-state to the off-state of the switch. The NEMS optical switch shows a switching time of 43.5 ns and a switching contrast of more than 25 dB. With its chip-scale integrability, the optical switch has potential applications in signal processing and high-speed optical communication networks.

Discrete Subspace Multiwindow Gabor Frames and Their Duals

This paper addresses discrete subspace multiwindow Gabor analysis. Such a scenario can model many practical signals and has potential applications in signal processing. In this paper, using a suitable Zak transform matrix we characterize discrete subspace mixed multi-window Gabor frames (Riesz bases and orthonormal bases) and their duals with Gabor structure. From this characterization, we can easily obtain frames by designing Zak transform matrices. In particular, for usual multi-window Gabor frames (i.e., all windows have the same time-frequency shifts), we characterize the uniqueness of Gabor dual of type I (type II) and also give a class of examples of Gabor frames and an explicit expression of their Gabor duals of type I (type II).

Spatial interplay of two four-wave mixing images

We investigate the interplay between the two components of the four-wave mixing (FWM) beams in a ladder-type three-level atomic system. The interplay, including the shift and splitting of the two FWM beams and their intensity modulation, depends on the frequency detuning and the angles as well as the powers of the pump fields. The x-directional splitting due to the cross-phase modulation and y-directional splitting because of electromagnetically induced gratings of FWM beams are investigated. Both the theoretical and experimental results exhibit that the spatial separation and the number of the FWM signals can be well controlled by additional dressing laser beams. Such studies not only can be very useful in better understanding the formation of spatial solitons but also have potential applications in signal processing.

Enhancement of Stochastic Resonance Using Optimization Theory

The traditional stochastic resonance is realized by adding an optimal amount of noise, while the parameter-tuning stochastic resonance is realized by optimally tuning the system parameters. This paper reveals the possibility to further enhance the stochastic resonance effect by tuning system parameters and adding noise at the same time using optimization theory. The further improvement of the maximal normalized power norm of the bistable double-well dynamic system with white Gaussian noise input can be converted to an optimization problem with constraints on system parameters and noise intensity, which is proven to have one and only one local maximum for the Gaussian-distributed weak input signal. This result is then extended to the arbitrary weak input signal case. For the purpose of practical implementation, a fast-converging optimization algorithm to search the optimal system parameters and noise intensity is also proposed. Finally, computer simulations are performed to verify its validity and demonstrate its potential applications in signal processing.

Time-Reversal signal processing: An overview

The development of time reversal (T/R) techniques both theoretically and pragmatically has heightened in interest over the last decade. Although the majority of the effort has been concentrated in analysis and proof-in-principle experiments, the evolution of these results have led to potential applications in signal processing. These range from the detection of flaws in nondestructive evaluation (NDE) and scatterers in ocean acoustics to the destruction of kidney stones in biomedical ultrasound. When the medium under investigation has quasihomogenous properties, imaging using the T/R operator has evolved as a viable entity. In this paper we present an overview of T/R from a signal processing perspective. Here we concentrate on the ability of the T/R to perform its primary function of ‘‘focusing’’ on the strongest scatterer. We show how the T/R properties provides us with the optimal spatio-temporal matched-filter property which is utilized in a wide variety of applications, especially in NDE, biomedical, and the newly investigated communications area. We note the relationship of T/R to the inverse solution providing an alternative in deconvolution-type problems.

Spatio-temporal co-operative phenomena in CNN arrays composed of chaotic circuits—simulation experiments

This paper presents results of a simulation study of complex dynamic phenomena in arrays composed of interacting chaotic circuits. Such arrays can be thought of as a new paradigm for modelling non-linear phenomena in spatially extended (high-dimensional or infinite-dimensional) systems and active media with potential applications in signal processing. Depending on the connection structure between the cells, the array can show disorganized hyperchaotic behaviour or spatially ordered chaotic waves. Patterns of behaviour depending on the excitation of the array and the connection structure are studied in this paper. Chua circuits are taken as standard chaotic cells.

Chaotic waves and spatio-temporal patterns in large arrays of doubly-coupled Chua's circuits

We investigate complex dynamic phenomena in arrays composed of interacting chaotic circuits. Such arrays can be thought of as a model of nonlinear phenomena in spatially extended (high-dimensional or infinite-dimensional) systems and active media with potential applications in signal processing. In this paper, we consider a particular structure of the network in which there exists double diffusive interactions between the cells. Such a double interaction can be considered as a paradigm and means for understanding very complex interactions existing in real systems where separate cells can communicate in various ways. We consider two basic cases where separate cells without coupling exhibit two different types of chaotic behavior. Depending on the connection structure, initial conditions imposed in the cells, the array exhibits various kinds of spatially ordered chaotic waves. Patterns of behavior depending on the excitation of the array and the connection structure are studied in this paper. Chua's circuits are taken as standard chaotic cells.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Systolic Lattice Processing By Optical Coupled-Wave Device Arrays

We propose to implement systolic sampled-data lattice processors optically by means of linear integrated optics arrays of coupled-wave devices such as switched directional couplers and TE-TM mode converters. Potential signal processing applications include discrete time and analog frequency filtering and optical pulse compression.

Optical signal processing with magnetostatic waves

Magneto-optical devices based on Bragg diffraction of light by magnetostatic waves (MSWs) offer the potential of large time-bandwidth optical signal processing at microwave frequencies of 1 to 20 GHz and higher. A thin-film integrated-optical configuration, with the interacting MSW and guided-optical wave both propagating in a common ferrite layer, is necessary to avoid shape-factor demagnetization effects. The underlying theory of the MSW-optical interaction is outlined, including the development of expressions for optical diffraction efficiency as a function of MSW power and frequency, device geometry, materials properties, and other relevant parameters. Recent experimental observations of anisotropic Bragg diffraction and collinear TE↔TM mode conversion induced by MSWs in yttrium iron garnet (YIG) thin films suggest that high-performance MSW integrated-optical devices are feasible. Diffraction levels as large as 4% (7-mm interaction length) and a modulation dynamic range of ∼30 db have been demonstrated. Potential signal processing applications are mentioned, including: spectrum analyzers, convolvers/correlators, deflectors, non-reciprocal optical isolators, and tunable narrowband optical filters. Advantages of these MSW-based devices over the analogous acousto-optical devices include: much greater operating frequencies, tuning through the MSW dispersion relation by varying either the rf frequency or the applied bias magnetic field, simple MSW transducer structures (e.g., a single stripline), and the potential for very high diffraction efficiencies.