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In this paper, two new Lagrange neural networks are proposed for compressed sensing. The first one is for the standard recovery of sparse signals. The second one is for the recovery of sparse signals with noise. By drawing into delay, we also derive two delayed Lagrange neural networks. Both the two networks are based on the l0 norm approximation. They can be implemented by circuits.

In this paper, neural network approach is addressed for signal reconstruction under the frame of compressed sensing. By introducing implicit variables, we convert the basis pursuit denoising model into a quadratic programming problem. Based on a class of generalized Fischer–Burmeister complementarity functions, we establish a neural network method for the signal reconstruction of compressed sensing. A projection neural network is also presented to recover the original signals. These two neural networks can be implemented using integrated circuits and two block diagrams of the neural networks are presented. Based on our proposed method, some potential applications of the compressed sensing are discussed.

The linear canonical transform (LCT) has been shown to be a powerful tool for optics and signal processing. In this paper, first, we present much briefer and more direct derivations of sampling relation for time-limited signal in LCT domain. Moreover, based on the sampling relation expansion in the LCT domain, the equivalent of the classical Fourier series (FS) for the LCT is derived directly. Then, the discrete-time linear canonical transform (DTLCT) is proposed through the dual extension of linear canonical series (LCS), which is the generalization of discrete-time Fourier transform (DTFT).

The Gibbs phenomenon describes the behavior of the partial sums of a Fourier series (FS) in a neighborhood of a simple discontinuity of the function expanded. In this paper, we investigate the Gibbs phenomenon for linear canonical series (LCS) in linear canonical transform (LCT) domain. We show that a similar phenomenon is observed for the LCS of a function with jump discontinuities. First, the convergence and Gibbs phenomenon of the LCS are discussed for the real parts of the LCS. It is showed that if a function is continuous, then there is no Gibbs phenomenon. Moreover, we proved that the uniform convergence of the LCS for a non-periodic analysis function in the smooth region. Then, we present a theorem that the Gibbs constant that arise for the LCS appears to be the same to that occurring in standard FS.

Linear canonical transforms (LCTs) are a family of integral transforms with wide application in optical, acoustical, electromagnetic, and other wave propagation problems. In this paper, a new kind of wave packet transform (WPT) associated with the LCT is proposed, this new WPT (WPTL) is defined based on the ideal of the LCT and the WPT. Some properties and physical meaning of the WPTL are investigated. In particular, we show a version of the resolution of the identity of WPTL. Moreover, the relationship between the WPTL and the Wigner distribution (WD) is derived. At last, we introduce the concept of the fractional wavepacketgram, which is defined as the modulus square of the WPTL. It is proved that the fractional wavepacketgram is a member of the Cohen class time–frequency distribution where the kernel is a scale dependent ambiguity function.

Fractional Fourier transform (FRFT) plays an important role in many fields of optics and signal processing. This paper considers the problem of real-time measurement of the spectrum of a signal in the FRFT domain. In this paper, we propose two approaches for real-time measurement of the FRFT of a signal based on modulation and bandpass filtering systems. The relation is established between the linear frequency modulation (LFM or chirp) spectrum and the FRFT of its envelope. In addition, two applications for spectrum measurement are presented in the FRFT domain. The LFM signal can be bandlimited in the Fourier transform (FT) domain through spectrum measurement associated with bandpass filtering method. The results can also be useful in the problems related to swept-frequency filter for measurement in the FRFT domain.

The wavelet transform (WT) and linear canonical transform (LCT) have been shown to be powerful tool for optics and signal processing. In this paper, firstly, we introduce a novel time-frequency transformation tool coined the generalized wavelet transform (GWT), based on the idea of the LCT and WT. Then, we derive some fundamental results of this transform, including its basis properties, inner product theorem and convolution theorem, inverse formula and admissibility condition. Further, we also discuss the time-fractional-frequency resolution of the GWT. The GWT is capable of representing signals in the time-fractional-frequency plane. Last, some potential applications of the GWT are also presented to show the advantage of the theory. The GWT can circumvent the limitations of the WT and the LCT.

The Gabor expansion (GE), which maps the time domain signal into the joint time and frequency domain, has been recognized as very useful for signal processing. However, sinusoidal analysis used in the traditional GE is not appropriate for a compact representation for chirp-type signals. In this paper, a generalized Gabor expansion (GGE) is proposed in order to rectify the limitations of the GE, the proposed expansion not only inherits the advantage of GE, but also has the capability of signal representations in the linear canonical transform (LCT) domain which is similar to the LCT. Basis functions of the proposed expansion are obtained via LCT basis. Compared with the traditional GE, the GGE can offer signal representations on a general, non-rectangular time–frequency plane tiling. Besides, the completeness and biorthogonality conditions of the GGE are derived.

The linear canonical transform (LCT) describes the effect of first-order quadratic phase optical system on a wave field. The classical multichannel sampling theorem for common bandlimited signals has been extended differently to bandlimited signals associated with LCT. However, a practical issue associated with the reconstruction of the original bandpass signal from multichannel samples in LCT domain still remains unresolved. The purpose of this paper is to introduce a practical multichannel sampling theorem for bandpass signals in LCT domain. The sampling expansion which is constructed by the ordinary convolution in the time domain can reduce the effect of spectral leakage and is easy to implement. The classical multichannel sampling theorem and the well-known sampling theorems for the LCT are shown to be special cases of it. Some potential applications of the multichannel sampling are also presented to show the advantage of the theory.

Linear canonical transform (LCT) form a three-parameter family of intergral transforms with wide application in optics. In this paper, we investigate the linear canonical Wigner distribution (LCWD) which is based on the LCT and the classical Wigner distribution (WD). Firstly, the definition of LCWD is discussed. Moreover, the transformation law for the LCWD through a first-order optical system is derived. This new phase-space distribution provides analysis of signals in both space and LCT domains simultaneously. Then, the main properties of LCWD are investigated in detail. Finally, the application of the LCWD is presented. The LCWD is found to be the appropriate phase-space distribution function for light-beam characterization in first-order optical system. Moreover, the moment matrix formalism for beam characterization is studied.

Fractional Fourier transform (FRFT) plays an important role in many field of optics and signal processing. The recently developed concept of two side fractional quaternion Fourier transform (FRQFT) based on quaternion algebra and FRFT has been found useful for signal and image processing. It is a generalization of the quaternion Fourier transform (QFT). Many properties of the FRQFT are already known, but an extension of the QFT's Plancherel theorem is still missing. The purpose of this paper is to introduce extensions of this theorem. Firstly, we establish scalar value Plancherel theorem for the FRQFT. Then, the concept of right side fractional quaternion Fourier transform (FRQFTr) is proposed. Furthermore, we establish quaternion value Plancherel theorem for the FRQFTr. The Plancherel theorems in QFT domain are shown to be special cases of the achieved results.

This paper addresses the problem of multidimensional signal reconstruction from generalized samples in fractional Fourier domain including the deterministic case and the stochastic case. The generalized sampling expansion is investigated for the case where the fractional bandlimited input depends on N real variable, i.e., f ( t ) = f ( t 1 , ⋯ , t N ) and is used as a common input to a parallel bank of m independent N dimensional linear fractional Fourier filters Hα,k(u), k = 1 , ⋯ , m . For the deterministic input, the input is assumed to have its N dimensional fractional Fourier transform bandlimited to the frequency rang |ui|≤Ωi, for i = 1 , ⋯ , N . If m, the number of fractional Fourier filters, is written as a product of positive integers in the form m = m 1 m 2 ⋯ m N , and if the fractional bandlimited input f(t) is processed by fractional Fourier filter Hα,k(u)resulting m outputs gk(t), then f(t) can be reconstructed in terms of the samples gk(nT), each output being sampled at the identical rates of Ω 1 csc α / m 1 π , Ω 2 csc α / m 2 π , ⋯ , Ω N csc α / m N π samples/second in t 1 , ⋯ , t N respectively. This contrasts with the rates of Ω 1 csc α / π , Ω 2 csc α / π , ⋯ , Ω N csc α / π in t 1 , ⋯ , t N needed for reconstruction of the unfiltered input f(t). Input sampling expansions in terms of samples of the output filters are given for both deterministic and stochastic inputs, the generalized sampling expansion for random input having the same form as for the deterministic case but interpreted in the mean-square sense. Our formulation and results are general and include derivative sampling and periodic nonuniform sampling in the fractional Fourier domain for multidimensional signals as special case. Finally, the potensional application of the multidimensional generalized sampling is presented to show the advantage of the theory. Especially, the application of multidimensional generalized sampling in the context of the image scaling about image super-resolution is also discussed. The simulation results of image scaling are also presented.

The linear canonical transform (LCT) describes the effect of first-order quadratic phase optical system on a wave field. In this paper, we address the problem of signal reconstruction from multichannel samples in the LCT domain based on a new convolution theorem. Firstly, a new convolution structure is proposed for the LCT, which states that a modified ordinary convolution in the time domain is equivalent to a simple multiplication operation for LCT and Fourier transform (FT). Moreover, it is expressible by a one dimensional integral and easy to implement in the designing of filters. The convolution theorem in FT domain is shown to be a special case of our achieved results. Then, a practical multichannel sampling expansion for band limited signal with the LCT is introduced. This sampling expansion which is constructed by the new convolution structure can reduce the effect of spectral leakage and is easy to implement. Last, the potential application of the multichannel sampling is presented to show the advantage of the theory. Especially, the application of multichannel sampling in the context of the image superresolution is also discussed. The simulation results of superresolution are also presented.

Linear canonical transforms (LCTs) are a family of integral transforms with wide application in optical, acoustical, electromagnetic, and other wave propagation problems. This paper addresses the problem of signal reconstruction from multichannel and periodic nonuniform samples in the LCT domain. Firstly, the multichannel sampling theorem (MST) for band-limited signals with the LCT is proposed based on multichannel system equations, which is the generalization of the well-known sampling theorem for the LCT. We consider the problem of reconstructing the signal from its samples which are acquired using a multichannel sampling scheme. For this purpose, we propose two alternatives. The first scheme is based on the conventional Fourier series and inverse LCT operation. The second is based on the conventional Fourier series and inverse Fourier transform (FT) operation. Moreover, the classical Papoulis MST in FT domain is shown to be special case of the achieved results. Since the periodic nonuniformly sampled signal in the LCT has valuable applications, the reconstruction expression for the periodic nonuniformly sampled signal has been then obtained by using the derived MST and the specific space-shifting property of the LCT. Last, the potential applications of the MST are presented to show the advantage of the theory.

A new transparent conducting light trapping structure with no free carrier absorption for solar cells is described. Indium oxide doped with molybdenum (IMO), prepared by the hollow cathode sputtering technique, exhibits high charge-carrier mobility up to 80 cm2/V s. No free-carrier absorption in the near infrared region has been found in the IMO. The superior long-wavelength transparency, however, is not sufficient for thin film Si solar cell applications. To obtain the highest possible short circuit current, the TCO needs to possess additional light trapping structure. Anisotropic etching of fiber texture oriented ZnO has been shown to result in an effective light trapping structure. Here we propose a bilayer structure that consists of light trapping-intrinsic ZnO and IMO (the ZnO/IMO bilayer). Both layers show low free-carrier absorption up to the wavelength of 1200 nm. We demonstrate the use of such a transparent conducting light trapping oxide (TCLO) in nanocrystalline (nc-Si:H) solar cells fabricated by a single chamber, batch-type PECVD process. Incorporation of such a transparent conducting light trapping bilayer can increase solar cell short-circuit current density (Jsc) by >30% compared to flat bilayers.

Single junction p-i-n Ac-Si:H solar cells were prepared in a low-cost, large-area single chamber radio frequency plasma enhanced chemical vapor deposition system. The effects of seeding processes on the growth of Ac-Si:H i-layers and performance of Ac-Si:H solar cells were investigated. Seeding processes, usually featured by highly hydrogen rich plasma, are effective in inducing the growth of Ac-Si:H ilayers. It has been demonstrated that p-layer seeding methods are preferable to i-layer seeding. While performance of Ac-Si:H solar cells produced by i-layer seeding methods was usually limited by very low fill factors, Ac-Si:H solar cells with good initial and stabilized conversion efficiencies were obtained by p-layer seeding. D 2005 Elsevier B.V. All rights reserved.

In this study, direct structural characterization of lc-Si:H solar cells deposited by conventional RF-PECVD was conducted using Raman spectroscopy, XRD, and AFM. Strong correlations between i-layer structural properties and device performance were established. A wide variety of i-layer microstructures, from mixed-phase Si:H to highly crystalline lc-Si:H, were revealed by Raman scattering. Micro-crystallinity obtained from Raman scattering, presented as Ic/Ia, proved to be sensitive to the microstructure of lcSi:H i-layers. Strong spatial non-uniformity of i-layer microstructure as well as variations in device performance were observed. It has been demonstrated here that stable, high performance lc-Si:H solar cells can only be obtained with i-layers being lc-Si:H, yet close to the lc-Si:H to mixed-phase Si:H transition edge where an optimum micro-crystallinity range (Ic/Ia at around 1.8) was identified. It was shown by XRD experiments that high performance, optimum lc-Si:H solar cells exhibit smaller grain sizes compared to solar cells with i-layers showing higher micro-crystallinity. Correlations among non-uniformity pattern, i-layer micro-crystallinity, and AFM surface morphologies were also observed. � 2004 Elsevier B.V. All rights reserved.

Fractional Fourier transform (FRFT) plays an important role in many fields of optics and signal processing. This paper considers the problem of reconstructing a fractional bandlimited signal with FRFT. We propose a novel reconstruction method for fractional bandlimited signals using the fractional Fourier series (FRFS). The advantage is that the sampling expansion can be deduced directly not based on the Shannon theorem. By utilizing the generalized form of Parseval’s relation for complex FRFS, we obtain the sampling expansion for fractional bandlimited signals with FRFT. We show that the sampling expansion for fractional bandlimited signals with FRFT is a special case of Parseval’s relation for complex FRFS.

Linear canonical transforms (LCTs) are a family of integral transforms with wide applications in optical, acoustical, electromagnetic, and other wave propagation problems. In this paper, we propose the random discrete linear canonical transform (RDLCT) by randomizing the kernel transform matrix of the discrete linear canonical transform (DLCT). The RDLCT inherits excellent mathematical properties from the DLCT along with some fantastic features of its own. It has a greater degree of randomness because of the randomization in terms of both eigenvectors and eigenvalues. Numerical simulations demonstrate that the RDLCT has an important feature that the magnitude and phase of its output are both random. As an important application of the RDLCT, it can be used for image encryption. The simulation results demonstrate that the proposed encryption method is a security-enhanced image encryption scheme.