The capacity-distortion (C-D) trade-offs for joint state and message communications (JSMC) over single- and multi-user channels are investigated, where the transmitters have access to generalized state information and feedback while the receivers jointly decode the messages and estimate the channel state. A coding scheme is proposed based on backward simultaneous decoding of messages and compressed state descriptions without the need for the Wyner-Ziv random binning technique. For the point-to-point channel, the proposed scheme results in the optimal C-D function. For the state-dependent discrete memoryless degraded broadcast channel (SD-DMDBC), the successive refinement method is adopted for designing multi-stage state descriptions. With the simultaneous decoding approach, the derived achievable region is shown to be larger than the region obtained by the sequential decoding approach that is utilized in existing works. As for the state-dependent discrete memoryless multiple access channel (SD-DMMAC), in addition to the proposed method, Willem’s coding strategy is applied to enable partial collaboration between transmitters through the feedback links. Moreover, the state descriptions are shown to enhance both communication and state estimation performance. Examples are provided for the derived results to verify the analysis, either numerically or analytically. With particular focus, simple but representative integrated sensing and communications (ISAC) systems are also considered, and their fundamental performance limits are studied.

This work proposes a unified framework for the joint estimation and control of mobile robots communicating over wireless channels. To this end, we consider a MIMO-OFDM point-to-point (P2P) link between a static base station (BS) and user equipment (UE) mounted on a robotic platform. In this setting, we study the particular scenario in which the robot must reach a target position while maintaining a high communication rate and estimating its pose from demodulated OFDM signals. We formulate this problem as a joint estimation and control task within a nonlinear, stochastic dynamical system. To address it, we leverage the iterative Linear Quadratic Gaussian (ILQG) method to derive a locally convergent and computationally efficient solution. Extensive simulations validate the proposed approach and shed light on the critical interplay between wireless communication and control, revealing an inherent trade-off between rate maximization and goal tracking, offering new insights into the co-design of next-generation autonomous, connected robotic systems.

This paper investigates the problem of computing capacity-cost ($\mathbf{C}-\mathbf{C}$) functions for continuous channels. Motivated by the Kullback-Leibler divergence (KLD) proximal reformulation of the classical Blahut-Arimoto (BA) algorithm, the Wasserstein distance is introduced to the proximal term for the continuous case, resulting in an iterative algorithm related to the Wasserstein gradient descent. Practical implementation involves moving particles along the negative gradient direction of the objective function's first variation in the Wasserstein space and approximating integrals by the importance sampling (IS) technique. Such formulation is also applied to the rate-distortion (R-D) function for continuous source spaces and thus provides a unified computation framework for both problems.

This paper aims at computing the capacity-distortion-cost (CDC) function for continuous memoryless channels, which is defined as the supremum of the mutual information between channel input and output, constrained by an input cost and an expected distortion of estimating channel state. Solving the optimization problem is challenging because the input distribution does not lie in a finite-dimensional Euclidean space and the optimal estimation function has no closed form in general. We propose to adopt the Wasserstein proximal point method and parametric models such as neural networks (NNs) to update the input distribution and estimation function alternately. To implement it in practice, the importance sampling (IS) technique is used to calculate integrals numerically, and the Wasserstein gradient descent is approximated by pushing forward particles. The algorithm is then applied to an integrated sensing and communications (ISAC) system, validating theoretical results at minimum and maximum distortion as well as the randomdeterministic trade-off.

This paper presents a novel approach to enhance sensing capabilities in UAV-enabled MIMO-OFDM ISAC systems by leveraging UAV mobility as a mono-static radar. By integrating uniform planar arrays (UPAs) and modeling the UAV dynamics in$S E(3)$, we address key challenges such as 3D space sensing and trajectory design. We propose a target tracking scheme using extended Kalman filtering (EKF) in$S E(3)$, along with trajectory optimization based on the conditional Posterior Cramer-Rao bound (CPCRB). Numerical results demonstrate the effectiveness of the proposed trajectory design in enhancing performance of target tracking and physical parameter estimation in UAVenabled MIMO-OFDM ISAC systems.

Split federated learning (SFL) is a compute-efficient paradigm in distributed machine learning (ML), where components of large ML models are outsourced to remote servers. A significant challenge in SFL, particularly when deployed over wireless channels, is the susceptibility of transmitted model parameters to adversarial jamming that could jeopardize the learning process. This is particularly pronounced for embedding parameters in large language models (LLMs) and vision language models (VLMs), which are learned feature vectors essential for domain understanding. In this paper, rigorous insights are provided into the influence of jamming embeddings in SFL by deriving an expression for the ML training loss divergence and showing that it is upper-bounded by the mean squared error (MSE). Based on this analysis, a physical layer framework is developed for resilient SFL with LLMs (R-SFLLM1) over wireless networks. R-SFLLM leverages wireless sensing data to gather information on the jamming directions-of-arrival (DoAs) for the purpose of devising a novel, sensing-assisted anti-jamming strategy while jointly optimizing beamforming, user scheduling, and resource allocation. Extensive experiments using both LLMs and VLMs demonstrate R-SFLLM’s effectiveness, achieving close-to-baseline performance across various natural language processing (NLP) and computer vision (CV) tasks, datasets, and modalities. The proposed methodology further introduces an adversarial training component, where controlled noise exposure significantly enhances the model’s resilience to perturbed parameters during training. The results show that more noise-sensitive models, such as RoBERTa, benefit from this feature, especially when resource allocation is unfair. It is also shown that worst-case jamming in particular translates into worst-case model outcomes, thereby necessitating the need for jamming-resilient SFL protocols.

In this paper, the problem of training large language models (LLMs) in split federated learning over real-world wireless networks is investigated. In the considered system, the embedding layers of an LLM are first computed at a client and then trans-mitted over a wireless MIMO-OFDM link to a server instance for further processing, continuing the forward- and initiating the backpropagation of the training to the originating client. Due to channel impairments and adversarial attacks, the server needs to compute the model losses and gradients using corrupted parameters such as embeddings in LLMs. The computation of the corresponding model losses is rigorously characterized using such perturbed embeddings and a direct connection to the communication mean-squared error (MSE) for models beyond simple neural networks is established. Subsequently, the communication errors are modeled as part of the training process, and a method to design beamforming, scheduling and power allocation is proposed, ensuring high task performance and model convergence even in the case of worst-case jamming. Results on two natural language processing tasks using different LLM architectures confirm the validity of the theoretical analysis and prove the effectiveness of the proposed wireless system design in terms of accuracy and F1 score.

This paper derives an achievable rate-distortion (RD) region for the state-dependent discrete memoryless multiple access channel (SD-DMMAC), where the generalized feedback and causal side information are present at encoders, and the decoder performs the joint task of message decoding and state estimation. The Markov coding and backward-forward two-stage decoding schemes are adopted in the proof. This scenario is shown to be capable of modeling various integrated sensing and communication (ISAC) applications, including the monostatic-uplink system and multi-modal sensor networks, which are then studied as examples.

In this paper, we investigate the fundamental limits of MIMO-OFDM integrated sensing and communications (ISAC) systems based on a Bayesian Cramér-Rao bound (BCRB) analysis. We derive the BCRB for joint channel parameter estimation and data symbol detection, in which a performance trade-off between both functionalities is observed. We formulate the optimization problem for a linear precoder design and propose the stochastic Riemannian gradient descent (SRGD) approach to solve the non-convex problem. We analyze the optimality conditions and show that SRGD ensures convergence with high probability. The simulation results verify our analyses and also demonstrate a fast convergence speed. Finally, the performance trade-off is illustrated and investigated.

This paper proposes a system architecture that embeds semantically-secure information-theoretic physical layer security (IT-PLS) non-intrusively into a 5G New Radio (NR) system in order to protect uplink transmissions via physical uplink control channels (PUCCH) against post-quantum eaves-dropping attacks. We implement a proof of concept of such system employing a code construction based on a modular coding scheme with a universal hash function that ensures semantic secrecy. We conduct link-level simulations of wiretap channels under different frequency-selective fading conditions and noise characteristics in order to evaluate the performance of such implementation for slow and fast fading scenarios. We model them using tapped delay line channel models involving rural and urban scenarios with line-of-sight (LOS) and non-LOS radio conditions, as specified by the 3GPP TR 38.901. We characterize such system by measuring the distinguishing error rate, block error rate, and secrecy outage probability under different time-varying fading channels. Our case study outlines how IT-PLS can be transparently embedded into future 6G systems as well.

We consider the task of converting different digital descriptions of analog bandlimited signals and systems into each other. Albeit fundamental, the problem of finding the proper digital description of analog information is crucial to digital twinning. The latter is an emerging concept in the field of digital data processing that is regularly mentioned as key approach in the optimization of future communication technologies like 6G. We prove that quantities such as the peak-to-average power ratio and the bounded-input/bounded-output norm, which determine the behavior of the real-world analog system, cannot generally be determined from the system's digital twin, depending on which of the above-mentioned descriptions is chosen. As a main result, we introduce a new digital description of analog signals and systems and prove it to be algorithmically more powerful than the traditional description based on Shannon's sampling approach.

Wireless channel sensing is one of the key enablers for integrated sensing and communication (ISAC) which helps communication networks understand the surrounding environment. In this work, we consider MIMO-OFDM systems and aim to design optimal and robust waveforms for accurate channel parameter estimation given allocated OFDM resources. The Fisher information matrix (FIM) is derived first, and the waveform design problem is formulated by maximizing the log determinant of the FIM. We then consider the uncertainty in the parameters and state the stochastic optimization problem for a robust design. We propose the Riemannian Exact Penalty Method via Smoothing (REPMS) and its stochastic version SREPMS to solve the constrained non-convex problems. In simulations, we show that the REPMS yields comparable results to the semidefinite relaxation (SDR) but with a much shorter running time. Finally, the designed robust waveforms using SREMPS are investigated, and are shown to have a good performance under channel perturbations.

The bandwidth of a signal is an important physical property that is of relevance in many signal- and information-theoretic applications. In this paper we study questions related to the computability of the bandwidth of computable bandlimited signals. To this end we employ the concept of Turing computability, which exactly describes what is theoretically feasible and can be computed on a digital computer. Recently, it has been shown that there exist computable bandlimited signals with finite energy, the actual bandwidth of which is not a computable number, and hence cannot be computed on a digital computer. In this work, we consider the most general class of band-limited signals, together with different computable descriptions thereof. Among other things, our analysis includes a characterization of the arithmetic complexity of the bandwidth of such signals and yields a negative answer to the question of whether it is at least possible to compute non-trivial upper or lower bounds for the bandwidth of a bandlimited signal. Furthermore, we relate the problem of bandwidth computation to the theory of oracle machines. In particular, we consider halting and totality oracles, which belong to the most frequently investigated oracle machines in the theory of computation.

This paper assesses the impact on the performance that information-theoretic physical layer security (IT-PLS) introduces when integrated into a 5G New Radio (NR) system. For this, we implement a wiretap code for IT-PLS based on a modular coding scheme that uses a universal-hash function in its security layer. The main advantage of this approach lies in its flexible integration into the lower layers of the 5G NR protocol stack without affecting the communication's reliability. Specifically, we use IT-PLS to secure the transmission of downlink control information by integrating an extra pre-coding security layer as part of the physical downlink control channel (PDCCH) procedures, thus not requiring any change of the 3GPP 38 series standard. We conduct experiments using a real-time open-source 5G NR standalone implementation and use software-defined radios for over-the-air transmissions in a controlled laboratory environment. The overhead added by IT-PLS is determined in terms of the latency introduced into the system, which is measured at the physical layer for an end-to-end (E2E) connection between the gNB and the user equipment.

The bandwidth of a signal is an important physical property that is of relevance in many signal processing applications. In this paper we study questions related to the computability of the bandwidth of bandlimited signals. To this end we employ the concept of Turing computability, which exactly describes what is theoretically feasible and can be computed on a digital machine. Recently, it has been shown that there exist bandlimited signals, the actual bandwidth of which cannot be algorithmically determined, i.e., computed on a digital machine. In this work, we consider the most general class of bandlimited signals and analyze whether it is at least possible to compute nontrivial upper or lower bounds for the actual bandwidth of its members. We show that this is not possible in general.

In this paper we use a seeded modular coding scheme for implementing physical layer security in a wiretap scenario. This modular scheme consists of a traditional coding layer and a security layer. For the traditional coding layer, we use a polar code. We evaluate the performance of the seeded modular coding scheme in an experimental setup with software defined radios and compare these results to simulation results. In order to assess the secrecy level of the scheme, we employ the distinguishing security metric. In our experiments, we compare the distinguishing error rate for different seeds and block lengths.

The bandwidth of a bandlimited signal is an important number that is relevant in many applications and concepts. For example, according to the Shannon sampling theorem, the bandwidth determines the minimum sampling rate that is required for a perfect reconstruction. In this paper we consider bandlimited signals with finite energy and bandlimited signals that are absolutely integrable and analyze whether the bandwidth of these signals can be determined algorithmically. We employ the concept of Turing computability, a theoretical model that describes the fundamental limits of what can be solved algorithmically on a digital hardware, and ask if, for a given computable bandlimited signal, it is possible to compute its bandwidth on a Turing machine. We show that this is not possible in general, because there exist computable bandlimited signals for which the bandwidth is a non-computable real number. Even the weaker question if the bandwidth of a given signal is smaller than a predefined value cannot be always answered algorithmically. Further, we prove that in the case where the bandwidth in not computable, it is even impossible to algorithmically determine a sequence of upper bounds that converges to the actual bandwidth of the signal. As a positive result, we show that the set of signals whose bandwidth is larger than some given value is semi-decidable.

In this paper we study the peak value problem, i.e., the task of computing the peak value of a bandlimited signal from its samples. The peak value problem is important, for example, in communications, where the peak value of the transmit signal has to be controlled in order that the amplifier is not overloaded, which would generate out-of-band radiation. We prove that the peak value of a computable bandlimited signal is computable on digital hardware if oversampling is used. The computability ensures that the approximation error can be effectively controlled. Further, we provide an algorithm that can be used to perform this computation and prove that oversampling is indeed necessary, because there exist signals for which the peak value problem cannot be algorithmically solved without oversampling. Hence, without oversampling the peak value of such signals cannot be computed on any digital hardware, including DSPs, FPGAs, and CPUs.

Shannon's sampling theorem is of high importance in signal processing, because it links the continuous-time and discrete-time worlds. For bandlimited signals we can switch from one domain into the other without loosing information. In this paper we analyze if and how this transition affects the computability of the signal. Computability is important in order that the approximation error can be controlled. We show that the computability of the signal is not always preserved. Further, we provide a simple necessary and sufficient condition for the computability of the continuous-time signal, and a simple canonical algorithm that can be used for the computation.

The bandwidth of a bandlimited signal is a key quantity that is relevant in numerous applications. For example, it determines the minimum sampling rate that is necessary to reconstruct a bandlimited signal from its samples. In this paper we study if it is possible to algorithmically determine the actual bandwidth of a bandlimited signal. We prove that this is not possible in general, because there exist bandlimited computable signals, which have a bandwidth that is not computable. To this end we employ the concept of Turing computability, which provides a theoretical model that describes the fundamental limits of any practically realizable digital hardware, such as CPUs, DSPs, or FPGAs. Further, we answer the weaker question if it can be algorithmically answered whether the bandwidth of a given signal is larger than a predefined value.

In this paper we study downsampling for bandlimited signals. Downsampling in the discrete-time domain corresponds to a removal of samples. For any downsampled signal that was created from a bandlimited signal with finite energy, we can always compute a bandlimited continuous-time signal such that the samples of this signal, taken at Nyquist rate, are equal to the downsampled discrete-time signal. However, as we show, this is no longer true for the space of bounded bandlimited signals that vanish at infinity. We explicitly construct a signal in this space, which after downsampling does not have a bounded bandlimited interpolation. This shows that downsampling in this signal space is an operation that can lead out of the set of discrete-time signals for which we have a one-to-one correspondence with continuous-time signals.

In this paper we study whether it is possible to decide algorithmically if the Fourier series of a continuous function converges uniformly. We show that this decision cannot be made algorithmically, because there exists no Turing machine that can decide for each and every continuous functions whether its Fourier series converges uniformly. Turing computability describes the theoretical feasible that can be implemented on a digital computer, hence the result shows that there exists no algorithm that can perform this decision.

The Fourier transform is an essential operation in information sciences. However, it can rarely be calculated in closed form. Nowadays, digital computers are used to compute the Fourier transform. In this paper we study the computability of the Fourier transform. We construct an absolutely integrable bandlimited function that is computable as an element of L2, such that its Fourier transform is not Turing computable. This means the Fourier transform is not computable on a digital computer, because we have no way of effectively controlling the approximation error. This result has consequences for algorithms that use the Fourier transform of bandlimited function, e.g., the computation of the convolution via a multiplication in the Fourier domain.

Large peak to average power ratios (PAPRs) are problematic for communication systems. One possible approach to control the PAPR is the tone reservation method. We analyze the tone reservation method for general complete orthonormal systems, and consider two solvability concepts: strong solvability and weak solvability. Strong solvability requires a rather strong control of the peak value of the transmit signal by the energy of the information signal, and thus might be to restrictive for practical applications. Therefore, the concept of weak solvability was introduced, which only requires the boundedness of the transmit signal. In this paper we prove that weak solvability and strong solvability are equivalent for arbitrary complete orthonormal systems.

In this paper we study the tone reservation technique for the reduction of the peak to average power ratio (PAPR) in code division multiple access (CDMA) systems that employ the Walsh functions. In the tone reservation method, the available carriers are partitioned into two sets, the information set, which carries the information, and the compensation set, which is used to reduce the PAPR. Central questions are: What is the best possible reduction of the PAPR? What is the optimal information set that achieves this reduction, and how can it be found? What is the general structure of the information set? So far, the answers were unknown. In this paper we completely solve these questions for CDMA systems that employ the Walsh functions. Interestingly, using the first N Rademacher functions is optimal under all sets of size N.

Our work is based on a recently introduced mathematical theory of deep convolutional neural networks (DCNNs). It was shown that DCNN s are stable with respect to deformations of bandlimited input functions. In the present paper, we generalize this result: We prove deformation stability on Sobolev spaces. Further, we show a weak form of deformation stability for the whole input space L2(Rd). The basic components of DCNNs are semi-discrete frames. For practical applications, a concrete choice is necessary. Therefore, we conclude our work by suggesting a construction method for semi-discrete frames based on bounded uniform partitions of unity (BUPUs) and give a specific example that uses B-splines.

In this paper we analyze the tone reservation method to reduce the peak to average power ratio (PAPR) in orthogonal frequency division multiplexing (OFDM) systems. We consider the case of a reduced compensation set, where only the positive carrier frequencies are used, and fully characterize the information sets for which the PAPR problem is solvable. It turns out that the reduction of the compensation set does not affect the solvability of the PAPR problem, however, the optimal constant are worse in general.

In this paper we analyze the convergence behavior of a sampling based system approximation process, where the time variable is in the argument of the signal and not in the argument of the bandlimited impulse response. We consider the Paley-Wiener space PWπ2of bandlimited signals with finite energy and stable linear time-invariant (LTI) systems, and show that there are signals and systems such that the approximation process diverges in the L2-norm, i.e., the norm of the signal space. We prove that the sets of signals and systems creating divergence are jointly spaceable, i.e., there exists an infinite dimensional closed subspace of PWπ2and an infinite dimensional closed subspace of the space of all stable LTI systems, such that the approximation process diverges for any non-zero pair of signal and system from these subspaces.

It is known that there exist signals in Paley-Wiener space PWπ1of bandlimited signals with absolutely integrable Fourier transform, for which the peak value of the Shannon sampling series diverges unboundedly. In this paper we analyze the structure of the set of signals which lead to strong divergence. Strong divergence is closely linked to the existence of adaptive methods. We prove that there exists an infinite dimensional closed subspace of PW1π1, all signals of which, except the zero signal, lead to strong divergence of the peak value of the Shannon sampling series.

In this paper we analyze the peak-to-average power ratio (PAPR) reduction by tone reservation for orthogonal frequency division multiplexing (OFDM) schemes. In addition to the strong solvability of the PAPR reduction problem, where the PAPR has to be bounded by some constant, we consider a weaker form of solvability, where only the boundedness of the peak value of the signal is required. We show that for OFDM both forms of solvability are equivalent. Further, we show that in the case where the PAPR problem is not solvable, the set of input signals that lead to an unbounded OFDM signal is a residual set. As a consequence, if the upper density of the carriers, used for information transmission, is positive, the set of input signals that lead to a bounded OFDM signal is a meager set.

The approximation of stable linear time-invariant (LTI) systems is studied for the Paley-Wiener space PWπ1of bandlimited functions with absolutely integrable Fourier transform. For pointwise sampling, it is known that there exist stable LTI systems and functions such that the approximation process diverges, regardless of the oversampling factor. Recently, it was shown that the divergence can be overcome by using more general measurement functionals that are based on a complete orthonormal system. However, this approach requires the approximation process to have an increased bandwidth. In this paper, a two channel approximation process is presented that is uniformly convergent for all stable LTI systems and all functions in PWπ1. An advantage of the two channel approach compared with the one channel approach is the reduction of the approximation bandwidth, which can be exactly the same as the input function bandwidth.

Knowing whether a reconstruction process, for example the Shannon sampling series, is strongly divergent in terms of the lim or only weakly divergent in terms of the lim sup is important, because strong divergence is linked to the non-existence of adaptive reconstruction processes. For non-adaptive reconstruction processes the existence is answered by the Banach-Steinhaus theory. However, the analysis of adaptive reconstruction processes is more difficult and not covered by the former theory. In this paper we consider the Paley-Wiener space PWπ1of bandlimited signals with absolutely integrable Fourier transform and analyze the structure of the set of signals for which the peak value of the Shannon sampling series is strongly divergent. We show that this set is lineable, i.e., that there exists an infinite dimensional subspace, all signals of which, except the zero signal, lead to strong divergence. Consequently, for all signals from this subspace, adaptivity in the number of samples that are used in the Shannon sampling series does not create a convergent reconstruction process.

Many divergence results for sampling series are in terms of the limit superior and not the limit. This leaves the possibility of a convergent subsequence. If there exists a convergent subsequence, adaptive signal processing techniques can be used. In this paper we study sampling-based signal reconstruction and system approximation processes for the space PWπ1of bandlimited signals with absolutely integrable Fourier transform. For all analyzed examples, which include the peak value of the Shannon and the conjugated Shannon sampling series, we prove strong divergence, i.e., divergence for all subsequences. Hence, adaptive signal processing techniques do not help in these cases. We further analyze whether an adaptive choice of the reconstruction functions in the oversampling case can improve the behavior.

The approximation of linear time-invariant (LTI) systems by sampling series is an important topic in signal processing. However, the convergence of the approximation series is not guaranteed: there exist stable LTI systems and bandlimited input signals such that the approximation series diverges, regardless of the oversampling factor and the sampling pattern. Recently, it has been shown that this divergence can be overcome by using measurement functionals instead of pointwise sampling. However, the bandwidth of the approximation series needs to be strictly larger than the signal bandwidth. In this paper we derive a two channel system approximation approach based on measurement functionals that converges for all stable LTI systems and all signals in the Paley-Wiener space PWπ1. Thanks to the two channel structure it is possible to achieve an approximation bandwidth that is equal to the signal bandwidth.

The approximation of linear time-invariant (LTI) systems by sampling series is an important topic in signal processing. However, the convergence of the approximation process is not guaranteed. In this paper we prove that for every sampling pattern that is a complete interpolating sequence there exists a universal stable LTI system such that for every oversampling factor there exists a bandlimited input signal such that the approximation process, which is used to approximate the output signal of the LTI system, diverges. This result shows a fundamental limit for the digital sampling-based implementation of systems.

The approximation of linear time-invariant (LTI) systems by sampling series is an important topic in signal processing. Recently, it was conjectured [1] and proved [2] that, for every sampling pattern that is a complete interpolating sequence, there exists a universal stable LTI system such that for every oversampling factor there exists a bandlimited input signal such that the approximation process, which is used to approximate the output signal of the LTI system, diverges. This instability of the approximation process shows a fundamental limit of sampling-based signals processing. However, as is shown in this paper, by using more general measurement functionals this divergence can be overcome.

Recently, a new constructive formula for the calculation of the Hilbert transform of bounded bandlimited signals was found. In this paper we use that formula to analyze the properties of the Hilbert transform. We further present a Fefferman-Stein-type decomposition theorem for bandlimited signals in BMO(R), i.e., bandlimited signals of bounded mean oscillation. Based on this decomposition we characterize the range of the Hilbert transform and derive properties of general bandlimited signals in BMO(R). We show the boundedness of bandpass signals in BMO(R) and the boundedness of the derivative of bandlimited signals in BMO(R). We further find the maximum growth of the Hilbert transform of bounded bandlimited signals.

The Hilbert transform is an important operator in signal processing, e.g., the definition of the “analytical signal” uses the Hilbert transform. In this paper we analyze the Hilbert transform for bounded bandlimited signals in B∞π. Although the common integral representation of the Hilbert transform may diverge for certain signals in B∞π, it is possible to define the Hilbert transform meaningfully for bounded signals. We employ a definition that is based on the H1-BMO(ℝ) duality. The problem of this abstract definition is that there exists no constructive procedure to calculate the Hilbert transform. However, for the subspace of bounded bandlimited signals, we can give an explicit formula for the calculation of the Hilbert transform. Further, we show that the Hilbert transform of a bounded bandlimited signal is still bandlimited but not necessarily bounded.

In this paper we analyze the reconstruction of bandlimited signals from their sine wave crossings by a sampling type reconstruction process. The reconstruction process is highly adapted to the signal which shall be reconstructed, because the reconstruction functions and the sampling points are implicitly generated by the signal. We show that the reconstruction process is uniformly convergent for all signals in the Paley-Wiener spaces VWπP, 1π1.

In this paper we analyze band-pass type systems that operate on bounded bandlimited signals. For a very general class of band-pass type systems, we prove that there exists no linear realization of the systems in this class. Since ideal band-pass type systems are included in this class, it follows that there exists no linear realization of ideal band-pass type systems. This result is obtained under very general assumptions. For example, we do not assume the systems to be time-invariance. Finally, it is shown that a non-linear realization of band-pass type systems is possible.

In this paper we analyze the convergence behavior of convolution-type system representations for the Paley-Wiener space PWπ1. We completely characterize all stable linear time-invariant (LTI) systems for which we have convergence in the distributional sense by giving a necessary and sufficient condition for convergence. Furthermore, we prove that there are stable LTI systems and signals in PWπ1for which the convolution integral and the convolution sum diverge even in a distributional sense. In signal processing, distributions are often used to show convergence. Surprisingly, here we are in a situation where distributions cannot be used to justify convergence.

The process of quantization generates a loss of information, and, thus, the original signal cannot be reconstructed exactly from the quantized samples in general. However, it is desirable to keep the error as small as possible. In this paper, the quantization error is quantified in terms of several distortion measures. All these measures employ the difference between the original signal and the reconstructed signal, which is obtained by bandlimited interpolation of the quantized samples. We assume that the signals are bandlimited and that the samples are taken at Nyquist rate. It is shown that for signals in the Paley-Wiener spacePW¿1, the supremum of the reconstructed signal, and, hence, the quantization error cannot be bounded in the sense that there exists a bounded subset ofPW¿1on which both quantities can increase unboundedly. This unexpected behavior is due to the nonlinearity of the quantization operator and the slow decay of the sinc function. The nonlinearity is essential for this behavior because every linear operator that fulfills a certain property of the quantization operator would otherwise have to be bounded. Furthermore, it is proven that for a fixed signal the possible quantization error increases as the quantization step size tends to zero. The treatment of the quantization error in this paper is completely deterministic.

The convergence behavior of a convolution representation of stable linear time-invariant (LTI) systems operating on the Zakai class of bandlimited signals is analyzed. It is shown that there are signals in the Zakai class for which the convolution integral diverges if the system is the Hilbert transform or the ideal low-pass filter with bandwidth less than or equal to the signal bandwidth. Moreover, using a previously obtained result of Habib, it is proved that the class of stable LTI systems that map the Zakai class into itself does not include the Hilbert transform and the ideal low-pass filter with bandwidth less than or equal to the signal bandwidth. Finally, it is shown that the concept of the analytical signal, which is used in communications, is problematic for the signal spaceZπ, because the operator for its computation is unbounded and discontinuous.

In this paper, the convergence behavior of the symmetric and the nonsymmetric Shannon sampling series is analyzed for bandlimited continuous-time wide-sense stationary stochastic processes that have absolutely continuous spectral measure. It is shown that the nonsymmetric sampling series converges in the mean-square sense uniformly on compact subsets of the real axis if and only if the power spectral density of the process fulfills a certain integrability condition. Moreover, if this condition is not fulfilled, then the pointwise mean-square approximation error of the nonsymmetric sampling series and the supremum of the mean-square approximation error over the real axis of the symmetric sampling series both diverge. This shows that there is a significant difference between the convergence behavior of the symmetric and the nonsymmetric sampling series.

In this paper we analyze the local and global convergence behavior of sampling series with non-equidistant sampling points for the Paley-Wiener space PWpi1and sampling patterns that are made of the zeros of sine-type functions. It is proven that the sampling series are locally uniformly convergent if no oversampling is used and globally uniformly convergent if oversampling is used. Furthermore, we show that oversampling is indeed necessary for global uniform convergence, because for every sampling pattern there exists a signal such that the peak value of the approximation error grows arbitrarily large if no oversampling is used. Finally, we use these findings to obtain similar results for the mean-square convergence behavior of sampling series for bandlimited wide-sense stationary stochastic processes.

We analyze sampling representations for translation invariant, linear and bounded systems, operating on band-limited signals. First, we characterize suitable kernels for reconstruction processes with and without oversampling. Then, we investigate the convergence behavior of general approximation processes, operating only on the samples and not on the whole continuous-time signal, for translation invariant, linear and bounded systems and signals in the Paley-Wiener space PWpi1. Recently, Habib analyzed similar questions for a larger space of functions, namely the Zakai class, but for a considerably smaller class of systems, not including the Hilbert transformation and the ideal low-pass filter. We show that for important systems there exists no approximation process that is uniformly convergent for all functions in PWpi1. Surprisingly, oversampling and the design of special kernels does not improve the convergence behavior in this case. Furthermore, a simple criterion is given for checking whether a certain approximation process is convergent for a given system or not.

Since the discovery of Shannonpsilas sampling theorem, signal and system representation has become an intense research topic. One task of system theory is to find efficient representations of signals and systems. In this paper time domain representations of stable linear time-invariant systems are analyzed. Although a frequency domain representation of such systems is always possible, the time domain representation is problematic. It is shown that the convolution integral diverges for certain systems and functions. Furthermore, we characterize the systems for which a time domain representation is possible by giving necessary and sufficient conditions for pointwise and uniform convergence.

In this paper we discuss the interplay between discrete-time and continuous-time signals and the question, whether certain properties of the signal in one domain carry over to the other domain. The Shannon sampling series and the more general Valiron interpolation series are the appropriate means to obtain the continuous-time, bandlimited signal out of its samples, i.e., the discrete-time signal. Furthermore, we investigate the symmetric sampling series and the behavior of the non-symmetric sampling series, which follows from the properties of the projection operator. It is well known, that the space of discrete-time signals with finite energy and the space of continuous- time, bandlimited signals with finite energy are isomorphic. Thus, discrete-time and continuous-time, bandlimited signals with finite energy can be used interchangeably. This interchangeability is not restricted to finite energy signals. It is valid for a considerably larger class, but not for the space of bounded signals: Even if the discrete-time signal is bounded, the corresponding bandlimited interpolation can be unbounded. For the proof we explicitly state such a bounded discrete-time signal. Furthermore, we show not only that the Shannon sampling series diverges for this signal, but also that there is no bounded, bandlimited interpolation at all.

This paper presents a novel approach for automatic and robust object detection. It utilizes a component-based approach that combines techniques from both statistical and structural pattern recognition domain. While the component detection relies on Haar-like features and an AdaBoost trained classifier cascade, the topology verification is based on graph matching techniques. The system was applied to face detection and the experiments show its outstanding performance in comparison to conventional face detection approaches. Especially in the presence of partial occlusions, uneven illumination, and out-of-plane rotations, it yields higher robustness. Furthermore, this paper provides a comprehensive review of recent approaches for object detection and gives an overview of available databases for face detection.

Recent advances in processing and networking capabilities of computers have led to an accumulation of immense amounts of multimedia data such as images. One of the largest repositories for such data is the World Wide Web (WWW). We present Cortina, a large-scale image retrieval system for the WWW. It handles over 3 million images to date. The system retrieves images based on visual features and collateral text. We show that a search process which consists of an initial query-by-keyword or query-by-image and followed by relevance feedback on the visual appearance of the results is possible for large-scale data sets. We also show that it is superior to the pure text retrieval commonly used in large-scale systems. Semantic relationships in the data are explored and exploited by data mining, and multiple feature spaces are included in the search process.