. Let P = fP 0 ; : : : ; Pn\Gamma1 g denote a set of polynomials with complex coefficients. Let Z = fz 0 ; : : : ; z n\Gamma1 g ae C denote any set of sample points. For any f = (f 0 ; : : : ; fn\Gamma1 ) 2 C n the discrete polynomial transform of f (with respect to P and Z) is defined as the collection of sums, f b f(P 0 ); : : : ; b f(Pn\Gamma1 )g, where f(P j ) = hf; P j i = P n\Gamma1 i=0 f i P j (z i )w(i) for some associated weight function w. These sorts of transforms find important applications in areas such as medical imaging and signal processing. In this paper we present fast algorithms for computing discrete orthogonal polynomial transforms. For a system of N orthogonal polynomials of degree at most N \Gamma 1 we give an O(N log 2 N) algorithm for computing a discrete polynomial transform at an arbitrary set of points instead of the N 2 operations required by direct evaluation. Our algorithm depends only on the fact that orthogonal polynomial sets satisfy a thre...

We introduce a novel method of feature extraction for texture segmentation that relies on multi-channel wavelet frames and two-dimensional envelope detection. We describe and compare two algorithms for envelope detection based on (1) the Hilbert transform and (2) zero-crossings. We present criteria for filter selection and discuss quantitatively their effect on feature extraction. The performance of our method is demonstrated experimentally on samples of both natural and synthetic textures. Keywords--- Feature extraction, image segmentation, wavelet analysis. I. Introduction Features for texture representation are of crucial importance for accomplishing segmentation[1]. Previous multichannel approaches for texture feature extraction utilized the concept of spatial-frequency representation [2] [3], and have been supported by studies of the human visual system [4]. In these methods, both complex and real filters were used. Complex prolate spheroidal sequences were used as channel filter...

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. Generalized FFTs are efficient algorithms for computing a Fourier transform of a function defined on finite group, or a bandlimited function defined on a compact group. The development of such algorithms has been accompanied and motivated by a growing number of both potential and realized applications. This paper will attempt to survey some of these applications. Appendices include some more detailed examples. 1. A brief history The now "classical" Fast Fourier Transform (FFT) has a long and interesting history. Originally discovered by Gauss, and later made famous after being rediscovered by Cooley and Tukey [21], it may be viewed as an algorithm which efficiently computes the discrete Fourier transform or DFT. In between Gauss and Cooley-Tukey others developed special cases of the algorithm, usually motivated by the need to make efficient data analysis of one sort or another. To cite but a few examples, Gauss was interested in efficiently interpolating the orbits of asteroids [43...

In this paper, we introduce a new class of noise robust acoustic features derived from a new measure of autocorrelation, and explicitly exploiting the phase variation of the speech signal frame over time. This family of features, referred to as "Phase AutoCorrelation" (PAC) features, include PAC spectrum and PAC MFCC, among others. In regular autocorrelation based features, the correlation between two signal segments (signal vectors), separated by a particular time interval , is calculated as a dot product of these two vectors. In our proposed PAC approach, the angle between the two vectors is used as a measure of correlation. Since dot product is usually more affected by noise than the angle, it is expected that PAC-features will be more robust to noise. This is indeed significantly confirmed by the experimental results presented in this paper. The experiments were conducted on the Numbers 95 database, on which "stationary" (car) and "non-stationary" (factory) Noisex 92 noises were added with varying SNR. In most of the cases, without any specific tuning, PAC-MFCC features perform better.

Transmit beamforming with receive combining is a simple method for exploiting the significant diversity provided by multiple-input multiple-output (MIMO) systems, and the use of orthogonal frequency division multiplexing (OFDM) enables low complexity imple-mentation of this scheme over frequency selective MIMO channels. Optimal beamforming requires channel state information in the form of the beamforming vectors corresponding to all the OFDM subcarriers. In an attempt to reduce the amount of feedback informa-tion, we propose a new approach to transmit beamforming that combines partial feedback and beamformer interpolation. In the proposed architecture, the receiver sends a fraction of information about optimal beamforming vectors to the transmitter, and the trans-mitter computes the beamforming vectors for all subcarriers through modified spherical linear interpolation of the conveyed beamforming vectors. Simulation results show that the proposed beamforming method requires much less feedback information than optimal beamforming while it exhibits slight diversity loss compared to the latter. I.

The problem of blind separation of a convolutive mixture of speech signals is considered. Signal separation is performed in the frequency domain. Based on observations from amplitude spectrograms of speech signals, the notion of amplitude modulation correlation (`AMCor') across dierent frequency channels is introduced. From the corresponding principle of amplitude modulation decorrelation, a novel costfunction and an algorithm for convolutive blind source separation are derived. The algorithms' main features are discussed. Successful separation of synthetic data and of realroom recordings of speech is performed. The results of the latter are compared to the performance of previous algorithms on the same data. Audio examples are available from the authors' web page [2]. In: P. Pajunen and J. Karhunen (Eds.), `Proceedings of the second international workshop on independent component analysis and blind signal separation', June 1922, 2000, Helsinki, Finland, pp. 215220. 1. INTRODU...

We consider a finite-capacity ATM multiplexer in discrete-time domain. The input traffic is the superposition of the traffic from different classes. Each class is formed by a number of periodic input sources (e.g. voice or shaped VBR sources) which are of the same periodicity. We investigate the autocorrelation function and the power density spectrum to show traffic dependencies in the multiplexer output process. We derive an exact solution for the autocorrelation function and the power density spectrum of the multiplexer output process when only one traffic class is considered. We show that the algorithm for the finite-capacitymultiplexer can also be applied for the case of an infinitecapacity multiplexer when the number of buffer places is set to a sufficiently large but finite value. By numerical examples it is shown that considering ON/OFF input sources instead of periodic input sources lead only to slightchanges in the autocorrelation function and that the main characteristics of it are preserved. We propose an approximate analysis for more than one input traffic class which uses the exact results for one traffic class. The numerical results are compared to simulation results and are in good agreement. It turns out that the power density spectrum of the multiplexer output process can be used to determine how many sources of which periodicity deliver cells to the multiplexer input. Since the measurement of the power density spectrum can be performed by standard signal processing equipment the power density spectrum can be used for several control functions (e.g. routing, admission control) inside an ATM network.

Currently, most approaches to speech recognition are frame-based in that they represent speech as a temporal sequence of feature vectors. Although these approaches have been successful, they cannot easily incorporate complex modeling strategies that may further improve speech recognition performance. In contrast, segment-based approaches represent speech as a temporal graph of feature vectors and facilitate the incorporation of a wide range of modeling strategies. However, difficulties in segmentbased recognition have impeded the realization of potential advantages in modeling. This thesis

This paper introduces new techniques for the efficient computation of a Fourier transform on a finite group. We present a divide and conquer approach to the computation. The divide aspect uses factorizations of group elements to reduce the matrix sum of products for the Fourier transform to simpler sums of products. This is the separation of variables algorithm. The conquer aspect is the final computation of matrix products which we perform efficiently using a special form of the matrices. This form arises from the use of subgroup-adapted representations and their structure when evaluated at elements which lie in the centralizers of subgroups in a subgroup chain. We present a detailed analysis of the matrix multiplications arising in the calculation and obtain easy-to-use upper bounds for the complexity of our algorithm in terms of representation theoretic data for the group of interest. Our algorithm encompasses many of the known examples of fast Fourier transforms. We recover the b...