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### Browsing by Author "Selesnick, Ivan W."

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Item Automatic Generation of Prime Length FFT Programs(1996-01-01) Selesnick, Ivan W.; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)Show more We describe a set of programs for circular convolution and prime length FFTs that are short, possess great structure, share many computational procedures, and cover a large variety of lengths. The programs make clear the structure of the algorithms and clearly enumerate independent computational branches that can be performed in parallel. Moreover, each of these independent operations is made up of a sequence of sub-operations which can be implemented as vector/parallel operations. This is in contrast with previously existing programs for prime length FFTs: they consist of straight line code, no code is shared between them, and they can not be easily adapted for vector/parallel implementations. We have also developed a program that automatically generates these programs for prime length FFTs. This code generating program requires information only about a set of modules for computing cyclotomic convolutions.Show more Item Complex Wavelet Transforms with Allpass Filters(2003-08-20) Fernandes, Felix; Selesnick, Ivan W.; van Spaendonck, Rutger; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)Show more Complex discrete wavelet transforms have significant advantages over real wavelet transforms for certain signal processing problems. Two approaches to the implementation of complex wavelet transforms have been proposed earlier. Both approaches require discrete-time allpass systems having approximately linear-phase and (fractional) delay. This paper compares the results when different allpass systems are used. In the earlier work, maximally flat delay allpass systems were used. In this paper, it is shown that an allpass system designed according to the minimax criterion yields improvements for the complex discrete wavelet transforms.Show more Item Constrained FIR Filter Design for 2-band Filter Banks and Orthonormal Wavelets(1994-10-20) Markus, Lang; Selesnick, Ivan W.; Odegard, Jan E.; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)Show more 2-band paraunitary FIR filter banks can be used to generate a multiresolution analysis with compactly supported orthonormal (ON) wavelets. The filter design problem is formulated and solved (a) as a constrained L_{Â â ¡}optimization problem and (b) as a constrained L_{2}optimization problem which allows arbitrary compromises between an L_{2}and an L_{Â â ¡}approach with both of them as special cases. Additional flatness constraints can also be easily included. The L_{2}and the L_{Â â ¡}design are based on the Kuhn-Tucker (KT) conditions and the alternation theorem, respectively. Therefore, optimality of the solution is guaranteed. The method (a) is a simpler alternative to a known method. The method (b) solves a more general problem than the approaches known in the literature including all of them as special cases.Show more Item Constrained Least Square Design of FIR Filters Without Specified Transition Bands(1996-01-15) Selesnick, Ivan W.; Lang, Markus; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)Show more We consider the design of digital filters and discuss the inclusion of explicitly specified transition bands in the frequency domain design of FIR filters. We put forth the notion that explicitly specified transition bands have been introduced in the filter design literature as an indirect and sometimes inadequate approach for dealing with discontinuities in the desired frequency response. We also present a rapidly converging, robust, simple algorithm for the design of optimal peak constrained least square lowpass FIR filters that does not require the use of transition bands. This versatile algorithm will design linear and minimum phase FIR filters and gives the best*L*filter and a continuum of Chebyshev filters as special cases._{2}Show more Item Constrained Least Square Design of FIR Filters Without Specified Transition Bands(1995-01-15) Selesnick, Ivan W.; Lang, Markus; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)Show more We consider the design of digital filters and discuss the inclusion of explicitly specified transition bands in the frequency domain design of FIR filters. We put forth the notion that explicitly specified transition bands have been introduced in the filter design literature as an indirect and sometimes inadequate approach for dealing with discontinuities in the desired frequency response. We also present a rapidly converging, robust, simple algorithm for the design of optimal peak constrained least square lowpass FIR filters that does not require the use of transition bands. This versatile algorithm will design linear and minimum phase FIR filters and gives the best*L*filter and a continuum of Chebyshev filters as special cases._{2}Show more Item The Dual-Tree Complex Wavelet Transform(2005-11-01) Selesnick, Ivan W.; Baraniuk, Richard G.; Kingsbury, Nicholas G.; Digital Signal Processing (http://dsp.rice.edu/)Show more The paper discusses the theory behind the dual-tree transform, shows how complex wavelets with good properties can be designed, and illustrates a range of applications in signal and image processing. The authors use the complex number symbol C in CWT to avoid confusion with the often-used acronym CWT for the (different) continuous wavelet transform. The four fundamentals, intertwined shortcomings of wavelet transform and some solutions are also discussed. Several methods for filter design are described for dual-tree CWT that demonstrates with relatively short filters, an effective invertible approximately analytic wavelet transform can indeed be implemented using the dual-tree approach.Show more Item Exchange Algorithms that Complement the Parks-McClellan Algorithm for Linear Phase FIR Filter Design(1997-02-01) Selesnick, Ivan W.; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)Show more This paper describes an exchange algorithm for the frequency domain design of linear phase FIR equiripple filters where the Chebyshev error in each band is specified. The algorithm is a hybrid of the algorithm of Hofstetter, Oppenheim and Siegel and the Parks-McClellan algorithm. The paper also describes a modification of the Parks-McClellan algorithm where either the passband or the stopband ripple size is specified and the other is minimized.Show more Item Extending Winograd's Small Convolution Algorithm to Longer Lengths(1994-01-15) Selesnick, Ivan W.; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)Show more For short data sequences, Winograd's convolution algorithms attaining the minimum number of multiplications also attain a low number of additions, making them very efficient. However, for longer lengths they require a larger number of additions. Winograd's approach is usually extended to longer lengths by using a nesting approach such as the Agarwal-Cooley or Split-Nesting algorithms. Although these nesting algorithms are organizationally quite simple, they do not make the greatest use of the factorability of the data sequence length. The algorithm proposed it this paper adheres to Winograd's original approach more closely than do the nesting algorithms. By evaluating polynomials over simple matrices we retain, in algorithms for longer lengths, the basic structure and strategy of Winograd's approach.Show more Item Generalized Digital Butterworth Filter Design(1995-01-15) Selesnick, Ivan W.; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)Show more This paper presents a formula-based method for the design of IIR filters having more zeros than (nontrivial) poles. The filters are designed so that their square magnitude frequency responses are maximally-flat at*m*= 0 and at*m*=*pi*and are thereby generalizations of classical digital Butterworth filters. A main result of the paper is that, for a specified half-magnitude frequency and a specified number of zeros, there is only one valid way in which to split the zeros between*z*= -1 and the passband. Moreover, for a specified number of zeros and a specified half-magnitude frequency, the method directly determines the appropriate way to split the zeros between*z*= -1 and the passband. IIR filters having more zeros than poles are of interest, because often, to obtain a good trade-off between performance and the expense of implementation, just a few poles are best.Show more Item Generalized Digital Butterworth Filter Design(1996-01-15) Selesnick, Ivan W.; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)Show more This paper presents a formula-based method for the design of IIR filters having more zeros than (nontrivial) poles. The filters are designed so that their square magnitude frequency responses are maximally-flat at*m*= 0 and at*m*=*pi*and are thereby generalizations of classical digital Butterworth filters. A main result of the paper is that, for a specified half-magnitude frequency and a specified number of zeros, there is only one valid way in which to split the zeros between*z*= -1 and the passband. Moreover, for a specified number of zeros and a specified half-magnitude frequency, the method directly determines the appropriate way to split the zeros between*z*= -1 and the passband. IIR filters having more zeros than poles are of interest, because often, to obtain a good trade-off between performance and the expense of implementation, just a few poles are best.Show more Item Magnitude Squared Design of Recursive Filters with the Chebyshev Norm Using a Constrained Rational Remez Algorithm(1994-10-01) Selesnick, Ivan W.; Lang, Markus; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)Show more We describe a Remez type exchange algorithm for the design of stable recursive filters for which the Chebyschev norm of H(w) - F(w) is minimized, where H(w) and F(w) are the realized and desired magnitude squared frequency responses. The number of poles and zeros can be chosen arbitrarily and the zeros do not have to lie on the unit circle. The algorithm allows us to design filters with non-conventional frequency responses with arbitrary weighting functions. It also gives optimal minimum phase FIR filters and Elliptic recursive filters as special cases. We discuss three main difficulties in the use of the Remez algorithm for recursive filter design and give ways to overcome them.Show more Item Magnitude Squared Design of Recursive Filters with the Chebyshev Norm Using a Constrained Rational Remez Algorithm(1994-05-01) Selesnick, Ivan W.; Lang, Markus; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)Show more We describe a Remez type exchange algorithm for the design of stable recursive filters for which the Chebyschev norm of H(w) - F(w) is minimized, where H(w) and F(w) are the realized and desired magnitude squared frequency responses. The number of poles and zeros can be chosen arbitrarily and the zeros do not have to lie on the unit circle. The algorithm allows us to design filters with non-conventional frequency responses with arbitrary weighting functions. It also gives optimal minimum phase FIR filters and Elliptic recursive filters as special cases. We discuss three main difficulties in the use of the Remez algorithm for recursive filter design and give ways to overcome them.Show more Item Nonlinear-Phase Maximally-Flat FIR Filter Deisgn(1996-09-20) Selesnick, Ivan W.; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)Show more This paper reports a new analytic technique for the design of nonlinear-phase maximally-flat lowpass FIR filters. By subjecting the response magnitude and the group delay (individually) to differing numbers of flatness constraints, a new family of filters is obtained. With these filters, the delay can be reduced while maintaining relatively constant group delay in the passband, without significantly altering the response magnitude.Show more Item Wavelet Based Speckle Reduction with Applications to SAR based ATD/R(1994-11-20) Guo, Haitao; Odegard, Jan E.; Lang, Markus; Gopinath, Ramesh A.; Selesnick, Ivan W.; Burrus, C. Sidney; Digital Signal Processing (http://dsp.rice.edu/)Show more This paper introduces a novel speckle reduction method based on thresholding the wavelet coefficients of the logarithmically transformed image. The method is computational efficient and can sinificantly reduce the speckle while preserving the resolution of the original image. Both soft and hard thresholding schemes are studied and the results are compared. When fully polarimetric SAR images are available, we proposed several approaches to combine the data from different polorizations to achieve even better performance. Wavelet processed imagery is shown to provide better detection performance for synthetic-aperture radar (SAR) based automatic target detection/recognition (ATD/R)problem.Show more