The FFT is used widely in signal processing for efficient computation of the Fourier transform (FT) of finitelength signals over a set of uniformly-spaced frequency locations. However, in many applications, one requires nonuniform sampling in the frequency domain, i.e.,a nonuniform FT . Several papers have described fast approximations for the nonuniform FT based on interpolating an oversampled FFT. This paper presents an interpolation method for the nonuniform FT that is optimal in the min-max sense of minimizing the worst-case approximation error over all signals of unit norm. The proposed method easily generalizes to multidimensional signals. Numerical results show that the min-max approach provides substantially lower approximation errors than conventional interpolation methods. The min-max criterion is also useful for optimizing the parameters of interpolation kernels such as the Kaiser-Bessel function.

proteomics

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Abstract. Digital signal processing has played a key role in the development of telecommunication systems over the last two decades. In recent years digital filter banks have been occupying an increasingly important role in both wireless and wireline communication systems. In this paper we review some of these applications of filter banks with special emphasis on discrete multitone modulation which has had an impact on high speed data communication over the twisted pair telephone line. We also review filter bank precoders which have been shown to be important for channel equalization applications. 1 1.

This paper proposes a simple equalizer for a recent multicarrier block transmission scheme which pads zeros (as opposed to a cyclic prefix) in each transmitted block. In the absence of high-power amplifier induced nonlinear effects, it is shown that the resulting scheme is simply the dual of the classical Cyclic Prefix OFDM transceiver. Comparison between the two systems that takes into account nonlinear distortions introduced by the clipper is also performed in the practical context of the wireless broadband 5GHz HiperLAN/2 system. Both the classical pilot-based as well as novel (semi-) blind subspace algorithms are applied for channel estimation. The advantage of subspace methods in lowering the variation of channel tracking is corroborated with simulations which verify practically accurate channel estimates along the bursts. 1.

It has been observed by many researchers that the protein-coding regions of DNA sequences exhibit a period-3 behavior due to codon structure. Identification of the period-3 regions helps in predicting the gene locations, and in fact allows the prediction of specific exons within the genes of eucaryotic cells. Traditionally these regions are identified with the help of techniques such as the windowed DFT. In this paper we consider the use of efficient digital filters for the same purpose. The filters can be designed not only to extract the period-3 component, but at the same time effectively eliminate the background 1If spectrum exhibited by nearly all DNA sequences.

The successive doubling method is an ecient procedure for the design of fast algorithms for orthogonal transforms of length N = r n , where the radix r is a power of 2. It reduces the algorithmic complexity from N 2 to N log r N . In this work we present a partitioned systolic architecture for the two standard radix successive doubling algorithms: ascend and descend communication patterns. The systolization and partitioning procedure we have used is made up of three actions. First, we transform the ow chart of the data for the successive doubling algorithm into a new chart of constant geometry in all its stages (n). We obtain the constant geometry by means of the perfect unshue (ascending algorithm) or shuf- e (descending algorithm) permutations of order log 2 r. We then carry out the decomposition of these permutations into elementary permutations, which can be implemented electronically. Finally, we project the index space of the data onto the index space associ...

The potential presence of fractional delays, non-minimum phase parts, and a colouring of the channel output can require adaptive equalizers to adapt very long impulse responses. Besides resulting in a large computational complexity, this will in general cause slow convergence for LMS-type adaptive algorithms. In this paper, we address the equalization problem by a subband approach to reduce computational complexity and to improve convergence speed. We discuss, why amongst other possibilities of subband processing the oversampled approach is particularly appealing to significantly reduce computational complexity and improve convergence speed. Simulation results for a typical communication channels are presented and highlight the benefit of our method. 1. Introduction When data is transmitted through a channel, the characteristics of the channel generally create a signal distortion which may cause bit errors on the receiving side. Thus, in communication systems a filter is employed to...

This paper presents an efficient approach to adaptive system identification in undermodelled cases, ie. when the impulse response to be identified is too long to be represented by an adaptive FIR filter operating within the computational benchmarks of a DSP chip. Beyond computational savings gained from adaptive filtering in decimated subbands, the subband approach enables to use different filter lengths in the frequency bands through distribution of taps from an overall number of filter weights determined by the computational benchmark. Compared to a fullband filter of the same complexity, this method can greatly enhance the model representation of long impulse responses. 1 Introduction When identifying very long impulse responses with an adaptive filter implemented on a DSP, as eg. found in acoustic echo control, often the benchmark limits the identification to an undermodelled problem, where IIR filters are not applicable to the nature of the problem [6]. Two possibilities to reduc...

In this paper, we show that an NPR M-channel filter bank with a diagonal system inserted between the analysis and synthesis filterbanks, with appropriately chosen single--sided analysis and synthesis filters, may be used to decompose an arbitrary FIR system of order L into M FIR complex subband components each of order L/K, where K is the downsampling rate. This decomposition is at the expense of using complex arithmetic for the subband processing. The proposed filter bank structure has application in the identification and equalization of long channels, (such as those that occur in reverberative environments) where existing algorithms may be intractable. By reducing the order of the problem in the subbands, such problems become computationally feasible. The improved performance and reduced computational requirements afforded by the proposed method are verified using the acoustic echo cancellation (AEC) problem as an example.