A new class of two-channel biorthogonal filter banks and wavelet bases

We propose a novel framework for a new class of two-channel biorthogonal filter banks. The framework covers two useful subclasses: i) causal stable IIR filter banks. ii) linear phase FIR filter banks. There exists a very efficient structurally perfect reconstruction implementation for such a class. Filter banks of high frequency selectivity can be achieved by using the proposed framework with low complexity. The properties of such a class are discussed in detail. The design of the analysis/synthesis systems reduces to the design of a single transfer function. Very simple design methods are given both for FIR and IIR cases. Zeros of arbitrary multiplicity at aliasing frequency can be easily imposed, for the purpose of generating wavelets with regularity property. In the IIR case, two new classes of IIR maximally flat filters different from Butterworth filters are introduced. The filter coefficients are given in closed form. The wavelet bases corresponding to the biorthogonal systems are generated. the authors also provide a novel mapping of the proposed 1-D framework into 2-D. The mapping preserves the following: i) perfect reconstruction; ii) stability in the IIR case; iii) linear phase in the FIR case; iv) zeros at aliasing frequency; v) frequency characteristic of the filters

Design of near allpass strictly stable minimal phase real valued rational IIR filters

In this brief, a near-allpass strictly stable minimal-phase real-valued rational infinite-impulse response filter is designed so that the maximum absolute phase error is minimized subject to a specification on the maximum absolute allpass error. This problem is actually a minimax nonsmooth optimization problem subject to both linear and quadratic functional inequality constraints. To solve this problem, the nonsmooth cost function is first approximated by a smooth function, and then our previous proposed method is employed for solving the problem. Computer numerical simulation result shows that the designed filter satisfies all functional inequality constraints and achieves a small maximum absolute phase error

Verification of Magnitude and Phase Responses in Fixed-Point Digital Filters

In the digital signal processing (DSP) area, one of the most important tasks is digital filter design. Currently, this procedure is performed with the aid of computational tools, which generally assume filter coefficients represented with floating-point arithmetic. Nonetheless, during the implementation phase, which is often done in digital signal processors or field programmable gate arrays, the representation of the obtained coefficients can be carried out through integer or fixed-point arithmetic, which often results in unexpected behavior or even unstable filters. The present work addresses this issue and proposes a verification methodology based on the digital-system verifier (DSVerifier), with the goal of checking fixed-point digital filters w.r.t. implementation aspects. In particular, DSVerifier checks whether the number of bits used in coefficient representation will result in a filter with the same features specified during the design phase. Experimental results show that errors regarding frequency response and overflow are likely to be identified with the proposed methodology, which thus improves overall system's reliability

All-Pole Recursive Digital Filters Design Based on Ultraspherical Polynomials

A simple method for approximation of all-pole recursive digital filters, directly in digital domain, is described. Transfer function of these filters, referred to as Ultraspherical filters, is controlled by order of the Ultraspherical polynomial, nu. Parameter nu, restricted to be a nonnegative real number (nu ≥ 0), controls ripple peaks in the passband of the magnitude response and enables a trade-off between the passband loss and the group delay response of the resulting filter. Chebyshev filters of the first and of the second kind, and also Legendre and Butterworth filters are shown to be special cases of these allpole recursive digital filters. Closed form equations for the computation of the filter coefficients are provided. The design technique is illustrated with examples

Digital filter design using root moments for sum-of-all-pass structures from complete and partial specifications

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Transmission Loss of Phase-Shifted Fiber Bragg Gratins in Lossy Materials: A Theoretical and Experimental Investigation

Narrow linewidth transmission filters in lossy materials based phase-shifted fiber Bragg gratings have been investigated experimentally and analytically. A novel matrix technique has been developed in calculation of the transmission loss and linewidth. The elements of the matrix simply consist of the coefficients of the coupled mode equations. Simulation shows a small fiber loss could result in a significant transmission loss, which has not been explained properly yet to our knowledge. For phase-shifted gratings in erbium-doped fibers, the absorption could result in over 20 dB loss at transmission wavelengths. Such an approach can also be used to analyze cladding modes, radiation mode, and complex structure gratings

Implementation of a Two-Channel Maximally Decimated Filter Bank using Switched Capacitor Circuits

The aim of this paper is to describe the implementation of a two-channel filter bank (FB) using the switched capacitor (SC) technique considering real properties of operational amplifiers (OpAmps). The design procedure is presented and key recommendations for the implementation are given. The implementation procedure describes the design of two-channel filter bank using an IIR Cauer filter, conversion of IIR into the SC filters and the final implementation of the SC filters. The whole design and an SC circuit implementation is performed by a PraCAn package in Maple. To verify the whole filter bank, resulting real property circuit structures are completely simulated by WinSpice and ELDO simulators. The results confirm that perfect reconstruction conditions can be almost accepted for the filter bank implemented by the SC circuits. The phase response of the SC filter bank is not strictly linear due to the IIR filters. However, the final ripple of a magnitude frequency response in the passband is almost constant, app. 0.5 dB for a real circuit analysis

Design Optimization of Flattop Interleaver and Its Dispersion Compensation

The objective of this paper is to present a general strategy for design optimization of flattop interleavers, and dispersion compensation for the interleavers, in order to achieve superior optical performance. The interleaver is formed by two multi-cavity Gire-Tournois etalons (MC-GTE) in a Michelson Interferometer (MI). An interleaver that has m cavities in one etalon and n cavities in the other is called an mn-GTE interleaver. Our optimization strategy exploits the general flattop condition and the technique of ripple equalization. Any mn-GTE interleaver may be optimized. The spectral performance can be greatly improved by the optimization process. As an illustration, we present a comprehensive analysis for a 11-GTE and a 21-GTE interleaver. The analytical expressions for flattop conditions, peak and trough positions are derived for optimization. The optimal performance of the interleavers can be controlled by the reflection coefficients and the parameters m and n. To achieve low-dispersion mn-GTE flattop interleavers, we propose to use one additional MC-GTE as a dispersion compensator to compensate for the chromatic dispersion. The analytical expressions of group delays and chromatic dispersions for an MC-GTE interleaver are derived. The optimization strategy of dispersion-ripple equalization is explained. The results show that the dispersion performance can be tailored by changing the reflection coefficients of the MC-GTE, and the dispersion and bandwidth can be enhanced by increasing the number of cavities of the MC-GTE