nils-herrmann/clean_scirepeval huggingface dataset:
Best wavelet packet bases using rate-distortion criteria

For a given hierarchy of admissible quantizers, the authors show an efficient scheme for coding adaptive trees whose individual nodes spawn off descendants forming a disjoint and complete basis cover for the space spanned by their parent nodes. The scheme presented guarantees operation on the convex hull of the operational R-D curve for the admissible hierarchy of quantizers. Applications for this coding technique include the CMQW (Coifman, Meyer, Quake, and Wickerhauser, 1990) generalized multiresolution wavelet packet decomposition, iterative subband coders, and quadtree structures. An application to image processing involving quadtrees with a family of DCT (discrete cosine transform) bases has been demonstrated in a JPEG-like coding environment with good improvement shown over the static JPEG (Joint Photographic Experts Group) coding scheme.<<ETX>>
Compression of ECG as a Signal with Finite Rate of Innovation

Compression of ECG (electrocardiogram) as a signal with finite rate of innovation (FRI) is proposed in this paper. By modelling the ECG signal as the sum of bandlimited and nonuniform linear spline which contains finite rate of innovation (FRI), sampling theory is applied to achieve effective compression and reconstruction of ECG signal. The simulation results show that the performance of the algorithm is quite satisfactory in preserving the diagnostic information as compared to the classical sampling scheme which uses the sinc interpolation
High resolution acquisition methods for wideband communication systems

We consider the problem of low-complexity timing synchronization in digital receivers for DS-CDMA and UWB systems operating over channels with single or multiple propagation paths. We extend some of our recent sampling results for certain classes of non-bandlimited signals and develop a method that takes advantage of transform techniques to perform propagation delay estimation from a low-dimensional subspace of a received signal, that is, by sampling below the traditional Nyquist rate. By lowering the sampling rate we reduce computational requirements compared to existing solutions, allow for slower A/D converters and significantly reduce the power consumption of digital receivers.
Image denoising via lossy compression and wavelet thresholding

Some past work has proposed to use lossy compression to remove noise, based on the rationale that a reasonable compression method retains the dominant signal features more than the randomness of the noise. Building on this theme, we explain why compression (via coefficient quantization) is appropriate for filtering noise from signal by making the connection that quantization of transform coefficients approximates the operation of wavelet thresholding for denoising. That is, denoising is mainly due to the zero-zone and that the full precision of the thresholded coefficients is of secondary importance. The method of quantization is facilitated by a criterion similar to Rissanen's minimum description length principle. An important issue is the threshold value of the zero-zone (and of wavelet thresholding). For a natural image, it has been observed that its subband coefficients can be well modeled by a Laplacian distribution. With this assumption, we derive a threshold which is easy to compute and is intuitive. Experiments show that the proposed threshold performs close to optimal thresholding.
Reconstruction of irregularly sampled discrete-time bandlimited signals with unknown sampling locations

The purpose of this paper is to develop methods that can reconstruct a bandlimited discrete-time signal from an irregular set of samples at unknown locations. We define a solution to the problem using first a geometric and then an algebraic point of view. We find the locations of the irregular set of samples by treating the problem as a combinatorial optimization problem. We employ an exhaustive method and two descent methods: the random search and cyclic coordinate methods. The numerical simulations were made on three types of irregular sets of locations: random sets; sets with jitter around a uniform set; and periodic nonuniform sets. Furthermore, for the periodic nonuniform set of locations, we develop a fast scheme that reduces the computational complexity of the problem by exploiting the periodic nonuniform structure of the sample locations in the DFT.
Packet video and its integration into the network architecture

Packet video is investigated from a systems point of view. The most important issues relating to its transmission are identified and studied in the context of a layered network architecture model, leading to a better understanding of the interactions between network and signal handling. The functions at a particular layer can thereby be made less dependent on network implementation and signal format. In the layered network model, the higher layers provide format conversion, hierarchical source coding, error recovery, resynchronization, cost/quality arbitration, session setup and tear-down, packetization, and multiplexing. Provisions from the network layers pertain mainly to real-time transmission. Special consideration is given to hierarchical source coding, error recovery, statistical behavior, and timing aspects. Simulation results indicating practical solutions to some of the issues raised are presented for a hierarchical packet-video subband coding system.
From Lagrange to Shannon... and back: another look at sampling [DSP Education]

Classical digital signal processing (DSP) lore tells us the tale of a continuous-time primeval signal, of its brutal sampling, and of the magic sine interpolation that, under the aegis of bandlimitedness, brings the original signal back to (continuous) life. This article switches the conventional viewpoint and cast discrete-time sequences in the lead role, with continuous-time signals entering the scene as a derived version of their gap-toothed archetypes. Some well-known but seldom-taught facts about interpolation and vector spaces are brought together and the classic sine reconstruction formula derived naturally from the Lagrange interpolation method are recalled. Such an elegant and mathematically simple result can have a great educational value in building a solid yet very intuitive grasp of the interplay between analog and digital signals.
Motion compensation of motion vectors

Motion compensation of image data has long been used for video compression. "Meta-motion" compensation, or motion compensation of motion vectors is presented as a new approach to data compression useful in very low bit rate (VLB) applications. Whereas present motion coding simply takes advantage of temporal redundancies among images, this new, computationally simple approach takes advantage of temporal redundancies between subsequent vector fields to efficiently code motion. Taking advantage of both the temporal redundancy of motion vectors and the "mapping" property of motion vectors, this method is shown to decrease the bit rate for vector coding in sequences with complex motion.
Low-sampling rate UWB channel characterization and synchronization

We consider the problem of low-sampling rate high-resolution channel estimation and timing for digital ultra-wideband (UWB) receivers. We extend some of our recent results in sampling of certain classes of parametric non-bandlimited signals and develop a frequency domain method for channel estimation and synchronization in ultra-wideband systems, which uses sub-Nyquist uniform sampling and well-studied computational procedures. In particular, the proposed method can be used for identification of more realistic channel models, where different propagation paths undergo different frequency-selective fading. Moreover, we show that it is possible to obtain high-resolution estimates of all relevant channel parameters by sampling a received signal below the traditional Nyquist rate. Our approach leads to faster acquisition compared to current digital solutions, allows for slower A/D converters, and potentially reduces power consumption of digital UWB receivers significantly.
Mobile sampling of bandlimited fields

We investigate a new method for the acquisition of bandlimited functions, which we call mobile sampling. A field is sampled by a mobile sensor that moves along a continuous path. In this context, it is possible to increase the spatial sampling rate along the sensor's path with marginal additional cost. Hence we assume that the sensors acquire the field values on its path at an arbitrarily high resolution. While in classical sampling theory the relevant performance metric is the average number of samples per unit area, in mobile sampling the main acquisition cost comes from the total distance that needs to be traveled by the moving sensor. We consider a performance metric tailored to mobile acquisition and study the mobile sampling problem with respect to this metric. The introduction of this metric completely changes the mathematical nature of the sampling problem. We present in a brief and simplified form recent results that show to which extent the classical Nyquist sampling theory admits a parallel in the context of mobile acquisition. We also provide a brief account of the main technical tools.
Optimal trellis-based buffered compression and fast approximations

The authors formalize the description of the buffer-constrained adaptive quantization problem. For a given set of admissible quantizers used to code a discrete nonstationary signal sequence in a buffer-constrained environment, they formulate the optimal solution. They also develop slightly suboptimal but much faster approximations. These solutions are valid for any globally minimum distortion criterion, which is additive over the individual elements of the sequence. As a first step, they define the problem as one of constrained, discrete optimization and establish its equivalence to some of the problems studied in the field of integer programming. Forward dynamic programming using the Viterbi algorithm is shown to provide a way of computing the optimal solution. Then, they provide a heuristic algorithm based on Lagrangian optimization using an operational rate-distortion framework that, with computing complexity reduced by an order of magnitude, approaches the optimally achievable performance. The algorithms can serve as a benchmark for assessing the performance of buffer control strategies and are useful for applications such as multimedia workstation displays, video encoding for CD-ROMs, and buffered JPEG coding environments, where processing delay is not a concern but decoding buffer size has to be minimized.
Sampling, sparsity, and inverse problems

Sampling is a central topic in signal processing, communications, and in all fields where the world is analog and computation is digital. The question is simple: When does a countable set of measurements allow a perfect and stable representation of a class of signals? This allows the reconstruction of the analog world, or interpolation. A related problem is when these measurements allow to solve inverse problems accurately, like source localization. Classic results concern bandlimited functions and shift-invariant subspaces, and use linear approximation. Recently, nonlinear methods have appeared, based on parametric methods and/or convex relaxation, which allow a broader class of sampling results. We review sampling of finite rate of innovation (FRI) signals, which are non-bandlimited continuous-time signals with a finite parametric representation. This leads to sharp results on sampling and reconstruction of such sparse continuous-time signals. We then explore performance bounds on retrieving sparse continuous-time signals buried in noise. While this is a classic estimation problem, we show sharper lower bounds for simple cases, indicating (i) there is a phase transition and (ii) current algorithms are close to the bounds. This leads to notions of resolution or resolvability. We then turn our attention to sampling problems where physics plays a central role. After all, many sensed signals are the solution of some PDE. In these cases, continuous-time or continuous-space modeling can be advantageous, be it to reduce the number of sensors and/or the sampling rate. First, we consider the wave equation, and review the fact that wave fields are essentially bandlimited in space-time domain. This can be used for critical sampling of acquisition or rendering of wave fields. We also show an acoustic source localization problem, where wideband frequency probing and finite element modeling show interesting localization power. Then, in a diffusion equation scenario, source localization using a sensor network can be addressed with a parametric approach, indicating trade-offs between spatial and temporal sampling densities. This can be used in air pollution monitoring and temperature sensing. In all these problems, the computational tools like FRI or CS come in handy when the modeling and the conditioning is adequate. Last but not least, the proof of the pudding is in experiments and/or real data sets.
Tilings of the time-frequency plane: construction of arbitrary orthogonal bases and fast tiling algorithms

The authors consider expansions which give arbitrary orthonormal tilings of the time-frequency plane. These differ from the short-time Fourier transform, wavelet transform, and wavelet packets tilings in that they change over time. They show how this can be achieved using time-varying orthogonal tree structures, which preserve orthogonality, even across transitions. The method is based on the construction of boundary and transition filters; these allow us to construct essentially arbitrary tilings. Time-varying modulated lapped transforms are a special case, where both boundary and overlapping solutions are possible with filters obtained by modulation. They present a double-tree algorithm which for a given signal decides on the best binary segmentation in both time and frequency. That is, it is a joint optimization of time and frequency splitting. The algorithm is optimal for additive cost functions (e.g., rate-distortion), and results in time-varying best bases, the main application of which is for compression of nonstationary signals. Experiments on test signals are presented.
Rate-distortion analysis of spike processes

Recent rate-distortion analyses of image transform coders are based on a trade-off between the lossless coding of coefficient positions versus the lossy coding of the coefficient values. We propose spike processes as a tool that allows a more fundamental trade-off, namely between lossy position coding and lossy value coding. We investigate the Hamming distortion case and give analytic results for single and multiple spikes. We then consider upper bounds for a single Gaussian spike with squared error distortion. The obtained results show a rate distortion behavior which switches from linear at low rates to exponential at high rates.
Toward self-organized mobile ad hoc networks: the terminodes project

This article provides a technical overview of mobile ad hoc networks and describes their long-term potential. It covers current research, and describes major technical challenges, including networking, real-time services, and software. It shows that by their very nature, mobile ad hoc networks can bring a paradigm shift in the way networks are organized and operated, and can even lead to a fundamental change in the relationships between information technology and societal organization. As an illustration of these concepts, the article also contains an overall description of our long-term research project, called terminodes.
On error-rate characteristics of oversampled A/D conversion

Accuracy of simple A/D conversion can be improved by refining either sampling interval or quantisation step. Although the former is more convenient for implementation reasons, the latter seems to be more efficient. When the quantization step tends to zero for a fixed sampling interval, the expected value of the quantization error decays exponentially as a function of the bit-rate B, E(e(t)/sup 2/)=O(exp(-2/spl alpha/B)). On the other hand, if the oversampling ratio is increased for a fixed quantization step the error behaves as E(e(t)/sup 2/)=O(1/B). We show that this inferior error-rate performance of oversampled A/D conversion is a consequence of inadequate reconstruction and encoding, and propose an efficient scheme for lossless encoding of quantized samples. With this encoding scheme the error of oversampled A/D conversion decays exponentially with the bit-rate.
Lower bound on the mean squared error in multi-loop /spl Sigma//spl Delta/ modulation with periodic bandlimited signals

Research has been devoted to optimal signal reconstruction by /spl Sigma//spl Delta/ modulation. Using classical linear filtering, the reconstruction mean squared error (MSE) asymptotically decreases with the oversampling ratio R by R/sup -(2n+1)/, where n is the order of the modulator. Using a nonlinear reconstruction scheme, an improvement of the MSE asymptotic behavior by 3 dB per octave of R has been observed for time-varying, periodic and bandlimited input signals. This implies an MSE of /spl Oscr/(R/sup -(2n+2)/). We show for the multi-loop configuration of the /spl Sigma//spl Delta/ modulation and with the same kind of input signals that the asymptotic behavior of the reconstruction MSE cannot be less than /spl Oscr/(R/sup -(2n+2)/), including optimal reconstruction.<<ETX>>
Split-radix algorithms for length-pm DFT's

The split-radix algorithm for the discrete Fourier trans- form of length-2"' is by now fairly popular. First, we give the reason why the split-radix algorithm is better than any single-radix algorithm on length-2" DFT's. Then, the split-radix approach is generalized to length-p" DFT's. It is shown that whenever a radix-p2 outperforms a radix-p algorithm, then a radix-plp' algorithm will outperform both of them. As an example, a radix-3/9 algorithm is developed for length- 3"' DFT's.  HE calculation of the discrete Fourier transform TpT) via a fast algorithm depends on the length of the sequence on which the transform has to be evaluated. When the length N is the product of coprime factors (N = II N,, (Ni, N, ) = 0, i # j ), one generally uses Good's mapping (8) to obtain a multidimensional transform that can then be evaluated with the Winograd (20) or the prime factor (lo) algorithm (note that the Cooley-Tukey map- ping could be used as well, but would be less efficient). When the factors of the length are not coprime (typically when N is a power of a small prime number p), then the Cooley-Tukey mapping (2) must be used and leads to a radix-r algorithm (r being equal top or one of its powers). Examples are radix-2 or radix-4 algorithms for the length- 2" DFT. In this type of algorithm, a large part of the com- putational complexity arises from intermediate multipli- cations, the so-called twiddle factors ( 121. In this paper, we will be concerned with the second case (that is, N = p") and discuss so-called split-radix algorithms. Note that these cannot be obtained via the classical Cooley-Tukey mapping and that this might be the reason why they were discovered only recently. Split- radix algorithms for length-2" DFT's were introduced simultaneously by several authors in 1984 (4), ( 1 11, ( 181, (16) and lead to the lowest known number of operations (multiplications and additions) for DFT's on these lengths (21). Recently, a number of papers have explored the split-radix idea, for example, from an implementation point of view (6), ( 141, for real data (6), ( 151, (7), or for the computation of convolutions and Hartley transforms
Tight Weyl-Heisenberg frames in l2(Z)

Tight Weyl-Heisenberg frames in l/sup 2/(Z) are the tool for short-time Fourier analysis in discrete time. They are closely related to paraunitary modulated filter banks and are studied here using techniques of the filter bank theory. Good resolution of short-time Fourier analysis in the joint time-frequency plane is not attainable unless some redundancy is introduced. That is the reason for considering overcomplete Weyl-Heisenberg expansions. The main result of this correspondence is a complete parameterization of finite length tight Weyl-Heisenberg frames in l/sup 2/(Z) with arbitrary rational oversampling ratios. This parameterization follows from a factorization of polyphase matrices of paraunitary modulated filter banks, which is introduced first.
High-order balanced multiwavelets: theory, factorization, and design

This paper deals with multiwavelets and the different properties of approximation and smoothness associated with them. In particular, we focus on the important issue of the preservation of discrete-time polynomial signals by multifilterbanks. We introduce and detail the property of balancing for higher degree discrete-time polynomial signals and link it to a very natural factorization of the refinement mask of the lowpass synthesis multifilter. This factorization turns out to be the counterpart for multiwavelets of the well-known zeros at /spl pi/ condition in the usual (scalar) wavelet framework. The property of balancing also proves to be central to the different issues of the preservation of smooth signals by multifilterbanks, the approximation power of finitely generated multiresolution analyses, and the smoothness of the multiscaling functions and multiwavelets. Using these new results, we describe the construction of a family of orthogonal multiwavelets with symmetries and compact support that is indexed by increasing order of balancing. In addition, we also detail, for any given balancing order, the orthogonal multiwavelets with minimum-length multifilters.
Optimal buffer-constrained source quantization and fast approximations

The description of the buffer-constrained quantization problem is formalized. For a given set of admissible quantizers for coding a discrete nonstationary signal sequence in a buffer-constrained environment, and for any global distortion minimization criterion that is additive over the individual elements of the sequence, the optimal solution and slightly suboptimal but much faster approximations are formulated. The problem is first defined as one of constrained, discrete optimization, and its equivalence to some problems in integer programming is established. Dynamic programming using the Viterbi algorithm is shown to provide a way of computing the optimal solution. A heuristic algorithm based on Lagrangian optimization and using an operational rate-distortion framework that, with much-reduced computing complexity, approaches the optimally achievable SNR is provided.<<ETX>>
A framework for interactive courses and virtual laboratories

Theory and experimentation are both complementary in sciences. Where the former builds up a formal framework, the latter helps humans to develop their intuition. Hard-printed books are great supports for theorems and formulas repositories, but stay desperately static when providing examples. This paper presents some directions towards a framework for digital publishing, distance learning and computer-aided teaching. The interactive digital signal processing (DSP) book is built in this framework and provides a concrete example to the reader. The book, reachable at http://lcavwww.epfl.ch/DSPBook, is used as a digital support for a course taught by our lab to a third year undergraduate class in electrical engineering.