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Ljiljana Milic, Mihajlo Pupin Institute, Belgrade (Yugoslavia)
Miroslav Lutovac, IRITEL, Belgrade (Yugoslavia)
A new straightforward design of a special class of elliptic IIR filters is presented. The major goal is the complexity reduction of the realized digital filter. The multiplier coefficients are implemented with limited number of shift-and-add operations. This method is also called "multiplierless". Unlike classical design, a closed-form relations are derived giving relationships between the filter specification and preferred multiplier coefficients. At least a half of the coefficients can be implemented with the minimal number of shift-and-add operations without coefficient quantization. The second half of coefficients can be optimized without any influence on the values of the first half of the coefficients. A high attenuation margins and low-sensitive structures are used so that specification is still fulfilled after quantization of the second half of the multiplier coefficients.
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Matti Karjalainen, Helsinki University of Technology (Finland)
Aki Härmä, Helsinki University of Technology (Finland)
Unto K. Laine, Helsinki University of Technology (Finland)
Digital filters where unit delays are replaced with frequency-dependent delays, such as first order allpass sections, are often called warped filters since they implement filter specifications on a warped non-uniform frequency scale. Warped IIR (WIIR) filters cannot be realized directly due to delay-free loops. Specific solutions have been known that make WIIR filters realizable but no general approach has been available so far. In this paper we will explore the generation of such filters, including new filter structures. The robustness and computational efficiency of WIIR filters are studied and most potential applications are discussed.
ic972205.pdf ic972205.pdf TOPIvan W. Selesnick, Rice University (U.S.A.)
This paper introduces a new set of exchange rules for a Remez-like algorithm for the Chebyshev design of IIR digital filters. It is explained that the essential difficulty, in applying the Remez algorithm to rational functions, is that on some iteration, there may be no solution to the interpolation problem for which the denominator is strictly non-zero in the interval of approximation. Then the usual procedure for updating the interpolation points can not be applied. The new rules for updating the interpolation points address precisely this problem for the two-pole case. It is shown with examples that, when the Remez-like algorithm of Hofstetter et al. is applied to rational functions, there is a way to update the interpolation points so that the algorithm converges rapidly, even when poles arise in the interval of approximation.
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Artur Krukowski, University of Westminster (U.K.)
Izzet Kale, University of Westminster (U.K.)
Richard C.S. Morling, University of Westminster (U.K.)
This paper addresses a new approach for the design of multiband filters with step like magnitude responses and extremely flat, weighted passbands down to microdBs. Our new technique can also be used for the multiband step-wise approximation of arbitrary filter magnitude responses with precise transition band control. One marked advantage of the technique is that our basic building blocks are the modified polyphase (IIR) filters as reported by Harris and Constantinides. The points of transition from one flat-top to another, namely the multiple transition bands of our filter are completely free of cross-over oscillations. One other advantage of this technique is that we are not confined to employing IIRs only. To this end perfect reconstruction FIR filters can also be used. In both the FIR and IIR cases our technique is general purpose, works for both real and complex valued filter coefficient cases. It is also advantegeous to other similar filter design techniques like Yulewalk.
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Zhongnong Jiang, Texas Instruments (U.S.A.)
Alan N. Willson, UCLA (U.S.A.)
By using a clock rate that is K times the data rate and with interleaved feedback of the output samples, a single expanded digital filter H(z^K) can be made equivalent to a cascade of k identical filters H^k(z) with 1leqkleqK. Whereas this novel pipelining/interleaving (PI) technique can equally be employed for implementing high-performance FIR filters, its main benefit lies in that more efficient high-speed IIR filters become achievable, though their highest possible data rates are still limited by the delays of the critical feedback loops. Hardware architectures and design examples with K = 2 are presented to show how the PI technique works for implementing high-speed IIR filters made as the sum of two allpass functions.
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Bojan Djokic, MOBTEL, Belgrade (Yugoslavia)
Miroslav Lutovac, IRITEL, Belgrade (Yugoslavia)
Miodrag Popovic, Faculty of EE, University of Belgrade (Yugoslavia)
This paper deals with the real-time implementation of the IIR filters having linear phase. Powell and Chau have devised an efficient method for the design and realization of real-time linear phase IIR filters using suitable modifications of the well-known time reversing technique. In their method, the input signal is divided into L-sample segments, time-reversed, and twice filtered using two IIR filter blocks whose transfer functions are the same. The performance of this techniques has been further improved by Willson and Orchard, where double zeros on the unit circle have been separated, giving better amplitude response in the stop-band and slightly smaller amplitude and phase distortions. In this paper, new improvements are described based on the reordering of polynomials in the numerator of the filter transfer function, or on the appropriate selection of the transfer function. The truncation noise, phase and amplitude errors of new realizations show considerable improvement over the previous solutions.
ic972221.pdf ic972221.pdf TOPAshraf Alkhairy, KACST-RICE (U.S.A.)
In this paper, we present an algorithm for the design of an optimal recursive digital filter with a specified magnitude frequency response. The method requires $O(N^2)$ computations to design a filter of size N, and exhibits numerical stability and quadratic convergence to the optimum within five iterations. The multiple exchange iterative algorithm uses the Chebyshev error criterion in the magnitude-squared frequency response domain, and has been developed using the interpolation theory and the alternation theorem for rational function approximation.
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Ahmet Kirac, Caltech (U.S.A.)
Palghat Vaidyanathan, Caltech (U.S.A.)
Energy compaction has proven to be an essential concept in signal-adapted data compression. In particular, optimization of orthonormal subband coders for a given power spectrum directly leads to optimal energy compaction filters. In this paper, we consider some new design methods and properties of optimal FIR energy compaction filters. In particular, we propose a very efficient method called the window method for the general M-channel case. The method does not involve any sophisticated optimization tools and terminates in a finite number of elementary steps. Compaction gains achieved by the method are very close to the optimal ones. As the filter order increases the filters of the proposed method converge to the optimum ideal compaction filters.
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Anush Yardim, University of Westminster (U.K.)
Gerald D. Cain, University of Westminster (U.K.)
Arnaud Lavergne, ESIEE (France)
Windowing is an attractive avenue for creating asymmetric FIR impulse response sequences for use as fractional-delay elements. However, traditional (symmetric) windows are not usable, leading to a need for offsetting and purpose-optimization of the windows' defining parameters. Here it is shown that as few as three terms of such a modified raised cosine window deliver enormous improvements over simple sinc fractional-sample delayors.
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Andrzej Tarczynski, University of Westminster (U.K.)
Vesa Välimäki, University of Westminster (U.K.)
Gerald D. Cain, University of Westminster (U.K.)
Filtering signals sampled on a grid which is nonuniformly distributed in the time domain is not a simple task since the filters coefficients have to be time varying. They must be updated at each sampling instant. The filtering becomes even more complicated when it has to be optimal (or at least suboptimal) in the sense of a certain design criterion. In this paper we present an effective algorithm for FIR filtering aiming at minimisation of the energy of the filtering error signal. The approach provides a solution which resembles Weighted Least Squares design method for FIR filters of uniformly sampled signals.
ic972237.pdf TOPManuel D. Ortigueira, INESC/IST (Portugal)
In this paper, the class of discrete linear systems is enlarged with the inclusion of the discrete-time fractional linear systems. These are systems described by fractional difference equations and fractional frequency responses. It is shown how to compute the impulse response and transfer function. The theory is supported by the Cauchy integrals that perform projections of the frequency response into or outside the unit circle. The presented formalism is similar to the usually followed.
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Nicholas Paul Murphy, University of Westminster (U.K.)
Artur Krukowski, University of Westminster (U.K.)
Andrzej Tarczynski, University of Westminster (U.K.)
In this paper we propose to use digital fractional sample delayers to perform high precision beam steering at the baseband sampling frequency. The major advantages of the proposed technique are that the fractional sample delayer used has a very flat magnitude response within the baseband width allowing greater than 20-bit resolution for a 35-tap Finite Impulse Response filter. It also has a delay which is continuously variable providing resolutions greater than 220,000ths of the baseband sampling time. Owing to the signal delay being performed at the baseband rate, elements with different delays may be placed in parallel, allowing for the formation of multiple beams (e.g. tracking and surveillance capability simultaneously).
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Chaouki Abdallah, University of New Mexico (U.S.A.)
Dalton S. Arantes, Univ. de Campinas (Brazil)
Gregory L. Heilemann, University of New Mexico (U.S.A.)
Don R. Hush, University of New Mexico (U.S.A.)
Ramiro Jordan, University of New Mexico (U.S.A.)
Roberto A. Lotufo, Univ. de Campinas (Brazil)
Neeraj Magotra, University of New Mexico (U.S.A.)
Howard Pollard, University of New Mexico (U.S.A.)
Edl Schamiloglu, University of New Mexico (U.S.A.)
Robert Whitman, University of New Mexico (U.S.A.)
The authors have developed an interactive environment for the creation and maintenance of dynamic, active multimedia-based teaching mechanisms. The Environment is designed to be user-friendly and to facilitate the creation o f educational material. This tool has already been used to create courses in Multi Dimensional Signal Processing (MDSP) by researchers working together while geographically separated.
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Martti Rahkila, HUT Acoustics (Finland)
Matti Karjalainen, HUT Acoustics (Finland)
This paper describes an interactive, self-study DSP tutorial package built for the World Wide Web (WWW, Web). The package includes concept explanation, graphical presentations, listening-ready audio examples and interactive exercises and demonstrations of basic concepts of signal processing. The WWW is a convenient and easy-to-use hypermedia tool. From the point of view of DSP education, the main problem is how to implement interactivity and signal processing. Our solution is to apply CGI (Common Gateway Interface) and Java in tasks that they are best suited for. A Common Lisp based WWW server CL-HTTP together with the QuickSig environment is used for providing signal processing routines in a CGI-like manner. Java applets are used for taking care of the user interface at the client end.
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