Efficient and multiplierless design of FIR filters with very sharp cutoff via maximally flat building blocks

A new design technique for linear-phase FIR filters, based on maximally flat buildiing blocks, is presented. The design technique does not involve iterative approximations and is, therefore, fast. It gives rise to filters that have a monotone stopband response, as required in some applications. The technique is partially based on an interpolative scheme. Implementation of the obtained filter designs requires a much smaller number of multiplications than maximally flat (MAXFLAT) FIR filters designed by the conventional approach. A technique based on FIR spectral transformations to design new multiplierless FIR filter structures is then advanced, and multiplierless implementations for sharp cutoff specifications are included

Efficient and multiplierless design of FIR filters with very sharp cutoff via maximally flat building blocks

A new design technique for linear-phase FIR filters, based on maximally flat buildiing blocks, is presented. The design technique does not involve iterative approximations and is, therefore, fast. It gives rise to filters that have a monotone stopband response, as required in some applications. The technique is partially based on an interpolative scheme. Implementation of the obtained filter designs requires a much smaller number of multiplications than maximally flat (MAXFLAT) FIR filters designed by the conventional approach. A technique based on FIR spectral transformations to design new multiplierless FIR filter structures is then advanced, and multiplierless implementations for sharp cutoff specifications are included

Optimal design of linear phase FIR digital filters with very flat passbands and equiripple stopbands

A new technique is presented for the design of digital FIR filters, with a prescribed degree of flatness in the passband, and a prescribed (equiripple) attenuation in the stopband. The design is based entirely on an appropriate use of the well-known Reméz-exchange algorithm for the design of weighted Chebyshev FIR filters. The extreme versatility of this algorithm is combined with certain "maximally flat" FIR filter building blocks, in order to generate a wide family of filters. The design technique directly leads to structures that have low passband sensitivity properties

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

Eigenfilters: A new approach to least-squares FIR filter design and applications including Nyquist filters

A new method of designing linear-phase FIR filters is proposed by minimizing a quadratic measure of the error in the passband and stopband. The method is based on the computation of an eigenvector of an appropriate real, symmetric, and positive-definite matrix. The proposed design procedure is general enough to incorporate both time- and frequency-domain constraints. For example, Nyquist filters can be easily designed using this approach. The design time for the new method is comparable to that of Remez exchange techniques. The passband and stopband errors in the frequency domain can be made equiripple by an iterative process, which involves feeding back the approximation error at each iteration. Several numerical design examples and comparisons to existing methods are presented, which demonstrate the usefulness of the present approach

Improved IIR Low-Pass Smoothers and Differentiators with Tunable Delay

Regression analysis using orthogonal polynomials in the time domain is used to derive closed-form expressions for causal and non-causal filters with an infinite impulse response (IIR) and a maximally-flat magnitude and delay response. The phase response of the resulting low-order smoothers and differentiators, with low-pass characteristics, may be tuned to yield the desired delay in the pass band or for zero gain at the Nyquist frequency. The filter response is improved when the shape of the exponential weighting function is modified and discrete associated Laguerre polynomials are used in the analysis. As an illustrative example, the derivative filters are used to generate an optical-flow field and to detect moving ground targets, in real video data collected from an airborne platform with an electro-optic sensor.Comment: To appear in Proc. International Conference on Digital Image Computing: Techniques and Applications (DICTA), Adelaide, 23rd-25th Nov. 201

Design of FIR digital filters with prescribed flatness and peak error constraints using second-order cone programming

This paper studies the design of digital finite impulse response (FIR) filters with prescribed flatness and peak design error constraints using second-order cone programming (SOCP). SOCP is a powerful convex optimization method, where linear and convex quadratic inequality constraints can readily be incorporated. It is utilized in this study for the optimal minimax and least squares design of linear-phase and low-delay (LD) FIR filters with prescribed magnitude flatness and peak design error. The proposed approach offers more flexibility than traditional maximally-flat approach for the tradeoff between the approximation error and the degree of design freedom. Using these results, new LD specialized filters such as digital differentiators, Hilbert Transformers, Mth band filters and variable digital filters with prescribed magnitude flatness constraints can also be derived. © 2005 IEEE.published_or_final_versio