Analog filters constitute indispensable components of analog circuits. Inspired by recent advances in digital filter design, this paper provides a flexible design for analog filters. All-pole filters have maximally flat passband, so our design minimizes their passband distortion. Analogously, maximally flat filters have maximally flat passband, so our design maximizes their stopband attenuation. Its particular cases provide flexible alternatives to the classical counterparts. Semidefinite program (SDP) formulations for the posed filter design problems are presented, which are efficiently solved by existing optimization software. Several examples and comparisons are provided to validate the viability of our design.

Optimized Analog Filter Designs With Flat Responses by Semidefinite Programming

A new design for linear phase diamond-shaped (DS) and circular-shaped (CS) 2D filters is developed. First, the frequency masks are efficiently constrained by 2D second-order trigonometric polynomials. Then semi-definite programming (SDP) of reasonably low dimension is employed to effectively express the filter specifications. Several numerical examples are provided to demonstrate the superior performance of our design in comparison with all other existing designs.

Design of Diamond and Circular Filters by Semi-definite Programming

Given a transfer function H(s) of order n, the celebrated bounded real lemma characterises the untractable semi-infinite programming (SIP) condition |H(jomega)|2 gesgamma 2forallomegaisinR of function bounded realness (BR) by a tractable semi-definite programming (SDP). Some recent results generalise this result for the SIP condition |H(jomega)|2 gesgamma 2forall|omega|gesomega of frequency-selective bounded realness (FSBR). The SDP characterisations are given at the expense of an introduced Lyapunov matrix variable of dimension n x n. As a result, the dimension of the resultant SDPs grows so quickly in respect to the function order, making them much less computationally tractable and practicable. Moreover, they do not allow to formulate synthesis problems as SDPs. In this paper, a completely new SDP characterizations for general FSBR for all-pole transfer functions is proposed. Our motivation is the design of infinite-impulse-response (IIR) filters involving a few of simutaneous FS-BRs. Our SDP characterizations are of moderate size and free from Lyapunov variables and thus allow to address problems involving transfer functions of arbitrary order. Examples are also provided to validate the effectiveness of the resulting SDP design formulation. Finally we also raise some issues arising with practicability of SDP for multi-dimensional filter design problems. In particular, any bilinear matrix inequality (BMI) optimization is shown to be solved by a SDP with any prescribed tolerance but the issue is dimensionality of this SDP

/pdf/a-dual-frequency-selective-bounded-real-lemma-and-its-50f16kqozr.pdf

A dual frequency-selective bounded real lemma and its applications to IIR filter design

This work presents an analytical design method for a category of two-dimensional IIR filters, specifically with circular symmetry, which have useful applications in image processing. The design is based on efficient digital elliptic filters, used as 1D prototypes, to which some complex frequency transformations are applied; this allows to obtain directly a factored form of the transfer function for the 2D circularly-symmetric filter. The design procedure involves some accurate approximations, but no global optimization algorithm. As a result, the 2D filter matrices are derived. The filter has the advantage of being adjustable, as its bandwidth is determined by a parameter which appears in the filter coefficients. The designed 2D filters have an accurate circular shape, exhibiting very low distortions even near the margins of the frequency plane, and are efficient, of high selectivity and relatively low order. The designed filters can be used as a bank of circular filters, useful in a multi-resolution analysis of an image. To prove their filtering capabilities, simulation results are provided for circular filtering of a biomedical image, namely a retina angiogram.

Circular IIR Filter Design and Applications in Biomedical Image Analysis

This paper proposes an analytic design method for a class of 2D recursive filters, namely with directional and square-shaped frequency response. The design technique is based on a specified 1D digital prototype filter and a complex frequency transformation which is determined using various rational approximations. Several design examples are presented for given specifications. The resulted filters are efficient and adjustable, being at the same time of low complexity and relatively high selectivity. These filters may have useful applications in image processing, like detecting lines with a given orientation from an image, as shown through simulation results on test images. The novelty of the proposed method consists in deriving the transfer function of the desired 2D filter only by applying successive frequency transformations to a prototype filter. Its advantages over most state-of-the-art design methods, which generally use global optimization numerical algorithms, is the filter tunability, and also its versatility; since the filter parameters, namely orientation and selectivity appear explicitly in the 2D filter matrices, they result directly for any specified parameters, therefore the design procedure does not need to be resumed every time from the start.

Analytic design of directional and square-shaped 2D IIR filters based on digital prototypes

A new design method for linear phase half-band diamond (DS) and fan-shaped (FS) 2-D filters is proposed. A general formulation for frequency mask constraints in different shapes using 2-D trigonometric curves is developed. This facilitates semi-definite programming (SDP) of moderate dimension for the design problem. Several examples are included to illustrate advantages of our method.

Design of Half-Band Diamond and Fan Filters by SDP

In this paper, a new technique for designing linear phase 2-D filter based on semi-definite programming (SDP) is proposed. This approach allows the design of 2-D filters with accurate cut-off frequency, subject to hard bounds on the frequency response to be achieved on a standard computer. Using the notion of 2-D trigonometric curves, we generalize the 2-D trigonometric Markov-Lukacs theorem to identify the pass-band and the stop-band in the region of support. The 2-D filter specifications are expressed as linear matrix inequalities. We also exploit convex duality to derive SDP formulations of reduced dimensions. Numerical examples illustrating the advantages of our method are also presented.

T.Q. Hung

Papers

Design of Diamond and Circular Filters by Semi-definite Programming

Design of Half-Band Diamond and Fan Filters by SDP

SDP for 2-d Filter Design: General Formulation and Dimension Reduction Techniques