Wireless networks equipped with the CSMA protocol are subject to collisions due to interference. For a given interference range, we investigate the tradeoff between collisions (hidden nodes) and unused capacity (exposed nodes). We show that the sensing range that maximizes throughput critically depends on the activation rate of nodes. For infinite line networks, we prove the existence of a threshold: When the activation rate is below this threshold, the optimal sensing range is small (to maximize spatial reuse). When the activation rate is above the threshold, the optimal sensing range is just large enough to preclude all collisions. Simulations suggest that this threshold policy extends to more complex linear and nonlinear topologies.

Wireless networks equipped with the CSMA protocol are subject to collisions due to interference. For a given interference range we investigate the tradeoff between collisions (hidden nodes) and unused capacity (exposed nodes). We show that the sensing range that maximizes throughput critically depends on the activation rate of nodes. For infinite line networks, we prove the existence of a threshold: When the activation rate is below this threshold the optimal sensing range is small (to maximize spatial reuse). When the activation rate is above the threshold the optimal sensing range is just large enough to preclude all collisions. Simulations suggest that this threshold policy extends to more complex linear and non-linear topologies.

Let g be a continuous, compactly supported function on such that the integer translates of g constitute a partition of unity. We show that the Gabor system (g,a,b), with window g and time-shift and frequency-shift parameters a,b>0 has no lower frame bound larger than 0 if b=2,3,... and a>0. In particular, (g,a,b) is not a Gabor frame if g is a continuous, compactly supported wavelet scaling function and if b=2,3,... and a>0. We give an example for our result for the case that g=B/sub 1/, the triangle function supported by [-1,1], by showing pictures of the canonical dual corresponding to (g,a,b) where ab=1/4 and b crosses the lines N=2,3,.

In many (audio) processing algorithms, involving manipulation of discrete-time signals, the performance can vary strongly over the repertoire that is used. This may be the case when the signals from the various channels are allowed to be strongly positively or negatively correlated. We propose and analyze a general formula for tracking the (time-dependent) correlation between two signals. Some special cases of this formula lead to classical results known from the literature, others are new. This formula is recursive in nature, and uses only the instantaneous values of the two signals, in a low-cost and low-complexity manner; in particular, there is no need to take square roots or to carry out divisions. Furthermore, this formula can be modified with respect to the occurrence of the two signals so as to further decrease the complexity, and increase ease of implementation. The latter modification comes at the expense that not the actual correlation is tracked, but, rather, a somewhat deformed version of it. To overcome this problem, we propose, for a number of instances of the tracking formula, a simple warping operation on the deformed correlation. Now we obtain, at least for sinusoidal signals, the correct value of the correlation coefficient. Special attention is paid to the convergence behavior of the algorithm for stationary signals and the dynamic behavior if there is a transition to another stationary state; the latter is considered to be important to study the tracking abilities to nonstationary signals. We illustrate tracking algorithm by using it for stereo music fragments, obtained from a number of digital audio recordings.

The generalized entropies of Renyi inspire new measures for estimating signal information and complexity in the time-frequency plane. When applied to a time-frequency representation (TFR) from Cohen's class or the affine class, the Renyi entropies conform closely to the notion of complexity that we use when visually inspecting time-frequency images. These measures possess several additional interesting and useful properties, such as accounting and cross-component and transformation invariances, that make them natural for time-frequency analysis. This paper comprises a detailed study of the properties and several potential applications of the Renyi entropies, with emphasis on the mathematical foundations for quadratic TFRs. In particular, for the Wigner distribution, we establish that there exist signals for which the measures are not well defined.

Recently, in the context of orthogonal frequency division multiplexing (OFDM), a new method (FAB-method) for constructing tight Gabor frames (with redundancy 2) from a (non-tight) Gaussian g was proposed by LeFloch et al. (see Proc. IEEE, vol.83, no.6, p.982-96, 1995). In this letter, we prove that the FAB-method yields the tight window function canonically associated to the Gaussian. We furthermore provide a necessary and sufficient condition on the initial window function g in the Zak transform domain for the FAB-method to yield a tight Gabor frame. This yields a characterization of all initial window functions g for which the FAB-method works.

We propose a new efficient method for the design of orthogonal and biorthogonal lapped transforms for image coding applications. It is shown how perception related constraints such as decay and smoothness of the filters' impulse responses can be incorporated in the optimization procedure. A decomposition of lapped transforms (orthogonal and biorthogonal) with 50% overlap leads to an efficient recursive optimization procedure, which is robust with respect to initial solutions. The importance of this decomposition lies in the fact that it allows to decouple the design of the even-symmetric and the odd-symmetric filters and hence drastically reduces the number of variables to be optimized. It furthermore reveals all the variables predetermined by perception related and coding-efficiency related constraints imposed on the filters. We present design and coding examples demonstrating the perceptual performance and the rate distortion performance of the resulting transforms.

We find an analytic expression for the maximum of the normalized entropy -/spl Sigma//sub i/spl epsiv/T/p/sub i/ln p/sub i///spl Sigma//sub i/spl epsiv/T/ip/sub i/ where the set T is the disjoint union of sets S/sub n/ of positive integers that are assigned probabilities P/sub n/, /spl Sigma//sub n/P/sub n/=1. This result is applied to the computation of the capacity of weakly (d,k)-constrained sequences that are allowed to violate the (d,k)-constraint with small probability.

The Capetanakis-Tsybakov-Mikhailov (1978, 1979) contention tree algorithm provides an efficient scheme for multiaccessing a broadcast-communication channel. This paper studies the statistical properties of multiple-access contention tree algorithms with ternary feedback for an arbitrary degree of node. The particular quantities under investigation are the number of levels required for a random contender to have successful access, as well as the number of levels and the number of contention frames required to provide access for all contenders. Through classical Fourier analysis approximations to both the average and the variance are calculated as a function of the number of contenders n. It is demonstrated that in the limit of large n these quantities do not converge to a fixed mode, but contain an oscillating term as well.

An important aspect of almost every watermarking system is the performance of the method by which watermark patterns are correlated with (derived features of) the suspect content. In the JAWS video watermarking system, developed at Philips Research, correlation is realized by symmetrical phase-only matched filtering. SPOMF detection has experimentally been shown to be an excellent correlation method. In this paper we address the problem of building a theoretical understanding of its performance. Being a non-linear correlation method, analysis of SPOMF detection performance is difficult. This paper is a first attempt to tackle the problem of deriving an analytical relationship between the energy of the embedded watermark and the reliability of detection. The theoretical results are compared with experimental results, and are found to be in good agreement.

This paper proposes a method to estimate the Integral Non-Linearity of A/D-converters from the lower order output Fourier coefficients of a sinusoidal input. In order to get a high quality estimate, the lower order Fourier coefficients have to be stabilized with respect to the rounding operation of the A/D-converter. For this we use a computationally efficient and easily applied method named wobbling.

Enumerative coding is an attractive algorithmic procedure for translating long source words into codewords and vice versa. The usage of long codewords makes it possible to approach a code rate which is as close as desired to Shannon's noiseless capacity of the constrained channel. Enumerative encoding is prone to massive error propagation as a single bit error could ruin entire decoded words. This contribution evaluates the effects of error propagation of the enumerative coding of runlength-limited sequences.

Enumerative coding is an attractive algorithmic procedure for translating long source words into codewords and vice versa. The usage of long codewords makes it possible to approach a code rate which is as close as desired to Shannon's noiseless capacity of the constrained channel. Enumerative encoding is prone to massive error propagation as a single bit error could ruin entire decoded words. This article evaluates the effects of error propagation of the enumerative coding of runlength limited sequences.

In this paper we propose a new technique, wobbling, for the stabilization of spectral ADC-test parameters with respect to offset and amplitude deviations of the sinusoidal stimulus. Wobbling aims at removing the effect of the rounding operation that takes place in an ADC, so that the measured harmonic distortion and noise amplitude can be truly ascribed to the intrinsic non-linearity and noise of the ADC. We compare the wobbling technique with subtractive and non-subtractive noise dithering, both from a performance and an implementation point-of-view. We present results of simulations and measurements validating the wobbling technique for use in a production environment.

We present an example of a positive function g with a positive Fourier transform g/spl circ/ and reasonable smoothness and decay properties such that (-1)/sup nm/exp(/spl pi/itm)g(t-n), n, m/spl isin/Z does not constitute a frame for L/sup 2/(R). We also give counterexamples for the statement that one can tell (in)definiteness of a Weyl-Heisenberg frame operator from (in)definiteness of its Weyl symbol.

It is shown that there is a tradeoff between the smoothness and decay properties of the dual functions, occurring in the lattice expansion problem. More precisely, it is shown that if g and g are dual, then (1) at least one of H/sup 1/2/ g and H/sup 1/2/ g is n in L/sup 2/(R), and (2) at least one of Hg and g is not in L/sup 2/(R). Here, H is the operator -1/(4 pi /sup 2/)d/sup 2//(dt/sup 2/)+t/sup 2/. The first result is a generalization of a theorem first stated by R.C. Balian (1987). The second result is new and relies heavily on the fact that, when G in W/sup 2,2/(S) with S=(-1/2, 1/2)*(-1/2, 1/2) and G(0), than 1/G not in L/sup 2/(S).>

It is shown how the Zak transform can be used to find nontrivial examples of functions f, g in L/sup 2/(R) with f*g identical to 0 identical to F*G, where F, G are the Fourier transforms of f, g, respectively. This is then used to exhibit a nontrivial pair of functions h, k in L/sup 2/(R), h not=k, such that mod h mod = mod k mod , mod H mod = mod K mod . A similar construction is used to find an abundance of nontrivial pairs of functions h, k in L/sup 2/(R), h not=k, with mod A/sub h/ mod = mod A/sub k/ mod or with mod W/sub h/ mod = mod W/sub k/ mod where A/sub h/, A/sub k/ and W/sub h/, W/sub k/ are the ambiguity functions and Wigner distributions of h, k, respectively. One of the examples of a pair of h, k in L/sup 2/(R), h not=k, with mod A/sub h/ mod = mod A/sub k/ mod is F.A. Grunbaum's (1981) example. In addition, nontrivial examples of functions g and signals f/sub 1/ not=f/sub 2/ such that f/sub 1/ and f/sub 2 /have the same spectrogram when using g as window have been found.>

It is shown that any periodic function m/sub 0/( zeta ) with nonnegative Fourier coefficients that satisfies the Smith-Barnwell conditions m/sub 0/(0)=1, mod m/sub 0/( zeta )/sup 2/+ mod m/sub 0/( zeta + pi ) mod /sup 2/=1 is of the form m/sub 0/( zeta )=exp(il zeta /2) cos k zeta /2 with l, k odd integers. As a consequence it is concluded that any nonnegative scaling function with orthonormal integer translates is of the form x/sub (k,k+1)/ with k in Z.>

The eigenstructure of bidiagonal Hessenberg-Toeplitz matrices is determined. These matrices occur as skeleton matrices of finite-state machines generating certain asymmetrically DC-constrained binary sequences that can be used for simulating pilot tracking tones in digital magnetic recording. The eigenstructure is used to calculate the Shannon upper bound to the entropy of the finite state machine as well as the power spectrum of the maxentropic process generated by it.>

Asymptotic results for the Perron-Frobenius eigenvalue of a nonnegative Hessenberg-Toeplitz matrix as the dimension of the matrix tends to infinity are given. The results are used and interpreted in terms of source entropies in the case where the Hessenberg-Toeplitz matrix arises as the transition matrix of a finite-state machine generating certain constrained sequences of +or-1's.>

We present short proofs and a generalization of the recently published results of Auslander and Tolimieri on ambiguity functions. The main ingredients for obtaining these shortcuts are elementary Hilbert space theory and unitarity of the ambiguity map.

In this paper algorithms for the restoration of unknown samples at known positions embedded in a neighbourhood of known samples are discussed. First this restoration problem is treated as a (non-adaptive) linear minimum variance estimation problem. It is shown that the optimal linear minimum variance interpolator for unknown samples from an autoregressive process uses only a finite neighbourhood of known samples, whereas in general this neighbourhood is infinite. Secondly, for signals that can be modelled as autoregressive processes an adaptive solution to the restoration problem is given.

We compare Gabor representation and the Wigner distribution on their merits for the time-frequency description of signals.

An interpolation method for restoring burst errors in discrete-time, band-limited signals is presented. The restoration is such that the restored signal has minimal out-of-band energy. The filter coefficients depend only on the burst length and on the size of the band to which the signal is assumed to be band-limited. The influence of additive noise and the effect of violation of the band-limitedness assumption is analysed with the aid of discrete prolate spheroidal sequences and wave functions. It is indicated for what combinations of values for noise power, burst length and bandwidth the method is still stable enough to be practicable.