HomeChair: T. Ramstad, Norwegian University of Science and Technology, Norway
HomeZoran D Cvetkovic, AT&T Labs (U.S.A.)
Weyl-Heisenberg frames are the tool for short-time Fourier analysis. These are generated from a prototype window function using translation on a rectangular grid in the time-frequency plane. Particularly appealing Weyl-Heisenberg frames are those which are tight as they allow for signal representations analogous to orthonormal expansions and have good numerical stability properties. Designing the window of a tight Weyl-Heisenberg frame requires optimization of the frequency characteristics of the window, usually some form of frequency selectivity, under a set of nonlinear constraints. For long windows that can be a formidable task, if not infeasible. We propose a new filter design method based on expansions with respect to prolate spheroidal sequences. The advantages of this new method are more and more pronounced as redundancy of the frame increases in reducing computational complexity and allowing for design of good filters which can be specified with few parameters.
ic982103.pdf (From Postscript)
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Robert M Nickel, The University of Michigan (U.S.A.)
Tzu-Hsien Sang, The University of Michigan (U.S.A.)
William J Williams, The University of Michigan (U.S.A.)
Quadratic time varying-spectral analysis methods that achieve a high resolution jointly in time and frequency generally suffer from interference terms that obscure the true location of the auto components in the resulting time-frequency representation.Unfortunately, as of now, there is no general mathematical model available for an exact distinction between cross-terms and autoterms. Consequently an attempt to suppress interferences can only rely on a few qualitative properties which are commonly associated with cross terms. Most of the reduced interference distributions that have been developed so far exploit the fact that cross terms tend to oscillate and can hence be suppressed by a properly chosen two-dimensional low pass filter. Besides the fact that cross-terms oscillate, they are also known to be responsible for all negative density values of a time-frequency distribution. Non of the currently existing methods addresses this characteristic. In this paper we introduce an entirely new approach that achieves a significant interference reduction by specifically exploiting the negative density structure of cross-terms.
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Shie Qian, National Instruments (U.S.A.)
Dapang Chen, National Instruments (U.S.A.)
Qinye Yin, Xi'an Jiaotong University (China)
The chirp function is one of the most fundamental functions in nature. Many natural events can be roughly approximated by a group of chirp functions. In this paper, we present a practical adaptive chirplet based signal approximation algorithm. Unlike the other chirplet decompositions known so far, the elementary chirplet functions employed in this algorithm are adaptive. Therefore, the resulting approximation could better match the underlying signal and uses fewer coefficients. The effectiveness of the algorithm is demonstrated by numerical simulations.
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Thomas W Parks, Cornell University (U.S.A.)
Michael S Richman, Cornell University (U.S.A.)
An analysis of a discrete time-frequency distribution yields a new periodic wide band probing signal for use in unknown system identification. The derivation is based on mathematical properties of the discrete Wigner distribution. Like the continuous distribution, the discrete version also satisfies the covariance property, meaning transformations in the time-frequency plane are equivalent to transformations in the time domain. By utilizing this property, the linearly swept frequency measurement is extended to discrete, periodic signals. The resulting probing signal possesses favorable characteristics such as a short illumination time requirement and good resistance to noise. The performance of the proposed probing method is compared with m-sequence methods and chirp signal methods.
ic982187.pdf (From Postscript) TOPDavid B.H. Tay, Nanyang Technological University (Singapore)
The design of 3-D multirate filter banks where the downsampling/upsampling is on the FCO (Face Centered Orthorhombic) lattice is addressed in this paper. With such a sampling lattice, the ideal 3-D subband of the low-pass filter is of the TRO (TRuncated Octahedron) shape. The transformation of variables has been shown previously to be an effective technique for designing M-D filter banks. We present a design technique for the transformation function using the multivariate Bernstein polynomial which provides good approximation to the TRO subband shape. The method is analytically based and does not require any optimization procedure. Closed form expressions are obtained for the filters of any order. Another advantage of this technique is that it yields filters with a flat frequency response at the aliasing frequency. The flatness is important for giving regular Discrete Wavelet Transform systems.
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Snezana Maslakovic, Stanford University (U.S.A.)
Ivan R. Linscott, Stanford University (U.S.A.)
Mitchell Oslick, Stanford University (U.S.A.)
Joseph D. Twicken, Stanford University (U.S.A.)
For signal-based design of orthonormal (ON) wavelets, an optimization of a cost function over an N-dimensional angle space is required. However: (1) the N-dim space includes both smooth and non-smooth wavelets; (2) many of the smooth wavelets are similar in shape. A more practical approach for some applications may be to construct a library of smooth ON wavelets in advance--a library that consists of representative wavelet shapes for a given filter length. Existing ON wavelet libraries (Daubechies, nearly-symmetric, Coiflets) provide only one wavelet for each filter length. We construct ON libraries using local variation to determine wavelet smoothness and the discrete inner product to discriminate between wavelet shapes. The relationship between library size and the similarity threshold is investigated for various filter lengths. We apply an entropy-based wavelet selection algorithm to an example signal set, and investigate compactness in the wavelet domain as a function of library size.
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Michael Sablatash, Communications Research Centre (Canada)
John H. Lodge, Communications Research Centre (Canada)
A set of desirable characteristics of a multicarrier spectrum-efficient bandwidth-on-demand multiplexer-demultiplexer pair for use in mobile satellite and personal communication systems is identified and described. New characteristics are the use of single VSB channels, design of multiplexer channels based on wavelet packet trees which have specified stopband attenuation, overlap of the multiplexer channel magnitude frequency responses at the 3-dB points for spectral efficiency, bandwidth on demand, reasonable lengths for the overall equivalent filters for each multiplexer-demultiplexer channel from input to receiver output, and low-complexity receivers. A multirate digital transmultiplexer is proposed consisting of a wavelet packet-based synthesis filter bank tree followed by a DFT polyphase synthesis filter bank at the transmitter, and a matching demultiplexer at the receiver. A simplified receiver for reception of one channel at a time is described. BER performances when there are phase and timing errors are given.
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Gianpaolo Evangelista, Univ. Federico II, Napoli (Italy)
Sergio Cavaliere, Univ. Federico II, Napoli (Italy)
In this paper we consider an extension of the wavelet transform leading to the construction of wavelets with arbitrary bandwidth. The new wavelets are complete, orthonormal and dyadic; nevertheless their bandwidth is not constrained to be one octave, rather it may be designed by selecting a set of parameters. The construction of the new bases starts in the discrete-time domain, exploiting properties of the Laguerre transform. Furthermore, we provide a procedure to define continuous-time warped wavelets. Flexibility of the bandwidth allocation allows for more and improved applications of the wavelet transform, such as signal coding, the design of auditory model based filterbanks and transient detection in pseudoperiodic signals, pointed out in the paper.
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