Synthesis of high-order bandpass filters based on coupled-resonator optical waveguides (CROWs)

We present a filter design formalism for the synthesis of coupled-resonator optical waveguide (CROW) filters. This formalism leads to expressions and a methodology for deriving the coupling coefficients of CROWs for the desired filter responses and is based on coupled-mode theory as well as the recursive properties of the coupling matrix. The coupling coefficients are universal and can be applied to various types of resonators. We describe a method for the conversion of the coupling coefficients to the parameters based on ring resonators and grating defect resonators. The designs of Butterworth and Bessel CROW filters are demonstrated as examples

Large-scale wave-front reconstruction for adaptive optics systems by use of a recursive filtering algorithm

We propose a new recursive filtering algorithm for wave-front reconstruction in a large-scale adaptive optics system. An embedding step is used in this recursive filtering algorithm to permit fast methods to be used for wave-front reconstruction on an annular aperture. This embedding step can be used alone with a direct residual error updating procedure or used with the preconditioned conjugate-gradient method as a preconditioning step. We derive the Hudgin and Fried filters for spectral-domain filtering, using the eigenvalue decomposition method. Using Monte Carlo simulations, we compare the performance of discrete Fourier transform domain filtering, discrete cosine transform domain filtering, multigrid, and alternative-direction-implicit methods in the embedding step of the recursive filtering algorithm. We also simulate the performance of this recursive filtering in a closed-loop adaptive optics system

2-D iteratively reweighted least squares lattice algorithm and its application to defect detection in textured images

In this paper, a 2-D iteratively reweighted least squares lattice algorithm, which is robust to the outliers, is introduced and is applied to defect detection problem in textured images. First, the philosophy of using different optimization functions that results in weighted least squares solution in the theory of 1-D robust regression is extended to 2-D. Then a new algorithm is derived which combines 2-D robust regression concepts with the 2-D recursive least squares lattice algorithm. With this approach, whatever the probability distribution of the prediction error may be, small weights are assigned to the outliers so that the least squares algorithm will be less sensitive to the outliers. Implementation of the proposed iteratively reweighted least squares lattice algorithm to the problem of defect detection in textured images is then considered. The performance evaluation, in terms of defect detection rate, demonstrates the importance of the proposed algorithm in reducing the effect of the outliers that generally correspond to false alarms in classification of textures as defective or nondefective

Efficient Synthesis of Room Acoustics via Scattering Delay Networks

An acoustic reverberator consisting of a network of delay lines connected via scattering junctions is proposed. All parameters of the reverberator are derived from physical properties of the enclosure it simulates. It allows for simulation of unequal and frequency-dependent wall absorption, as well as directional sources and microphones. The reverberator renders the first-order reflections exactly, while making progressively coarser approximations of higher-order reflections. The rate of energy decay is close to that obtained with the image method (IM) and consistent with the predictions of Sabine and Eyring equations. The time evolution of the normalized echo density, which was previously shown to be correlated with the perceived texture of reverberation, is also close to that of IM. However, its computational complexity is one to two orders of magnitude lower, comparable to the computational complexity of a feedback delay network (FDN), and its memory requirements are negligible

"Ideal" optical delay lines based on tailored-coupling and reflecting, coupled-resonator optical waveguides

We present a design of "ideal" optical delay lines (i.e., constant amplitude and constant group delay over the desired bandwidth). They are based on reflection from coupled-resonator optical waveguides (CROWs). The inter-resonator coupling coefficients are tailored and decrease monotonically with the distance from the input to realize all-pass Bessel filters. The tailored coupling coefficients result in a frequency-dependent propagating distance which compensates for the group velocity dispersion of CROWs. We present a simple formalism for deriving the time-domain coupling coefficients and convert these coefficients to field coupling coefficients of ring resonators. The reflecting CROWs possess a delay-bandwidth product of 0.5 per resonator, larger than that of any kind of transmitting CROW. In the presence of uniform gain, the gain enhanced by slow light propagation and the constant group delay result in efficient and dispersion-free amplifiers

Design of doubly-complementary IIR digital filters using a single complex allpass filter, with multirate applications

It is shown that a large class of real-coefficient doubly-complementary IIR transfer function pairs can be implemented by means of a single complex allpass filter. For a real input sequence, the real part of the output sequence corresponds to the output of one of the transfer functions G(z) (for example, lowpass), whereas the imaginary part of the output sequence corresponds to its "complementary" filter H(z)(for example, highpass). The resulting implementation is structurally lossless, and hence the implementations of G(z) and H(z) have very low passband sensitivity. Numerical design examples are included, and a typical numerical example shows that the new implementation with 4 bits per multiplier is considerably better than a direct form implementation with 9 bits per multiplier. Multirate filter bank applications (quadrature mirror filtering) are outlined

Orthogonal Wavelets via Filter Banks: Theory and Applications

Wavelets are used in many applications, including image processing, signal analysis and seismology. The critical problem is the representation of a signal using a small number of computable functions, such that it is represented in a concise and computationally efficient form. It is shown that wavelets are closely related to filter banks (sub band filtering) and that there is a direct analogy between multiresolution analysis in continuous time and a filter bank in discrete time. This provides a clear physical interpretation of the approximation and detail spaces of multiresolution analysis in terms of the frequency bands of a signal. Only orthogonal wavelets, which are derived from orthogonal filter banks, are discussed. Several examples and applications are considered