2020
This chapter begins with an introduction on z-transforms. The z-transform is the broadest concept for converting discrete-time series. The Laplace transform is the broadest concept for converting continuous-time processes. The inverse z-transform can be derived using the Cauchy integral theorem. The chapter also presents, synoptically, the basics of signal processing and then discusses real discretization processing and coding techniques. In practice, sampling consists of allowing the signal to pass over a very brief instant at regular times periods.
Cited by 1
Ivars Bilinskis · 2007
This chapter contains sections titled: Cross-interference Coefficients Taking the Cross-interference into Account Achievable Improvement and Typical Problems Parallel Computing Approach Mapping of the Cross-interference Coefficients
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Rachel Ward · Applied and numerical harmonic analysis · 2015
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P. L. Butzer · Applied optimization · 2002
Cited by 4
Lapuh, Rado · CERN Document Server (European Organization for Nuclear Research) · 2018
Cited by 1
Chen, Siheng, Varma, Rohan, Sandryhaila, Aliaksei et al. · KiltHub Repository · 2018
We propose a sampling theory for signals that are supported on either directed or undirected graphs. The theory follows the same paradigm as classical sampling theory. We show that the perfect recovery is possible for graph signals bandlimited under the graph Fourier transform, and the sampled signal coefficients form a new graph signal, whose corresponding graph structure is constructed from the original graph structure, preserving frequency contents. By imposing a specific structure on the graph, graph signals reduce to finite discrete-time signals and the proposed sampling theory works reduces to classical signal processing. We further establish the connection to frames with maximal robustness to erasures as well as compressed sensing, and show how to choose the optimal sampling operator, how random sampling works on circulant graphs and Erdos-R ˝ enyi graphs, ´ and how to handle full-band graph signals by using graph filter banks. We validate the proposed sampling theory on the simulated datasets of Erdos-R ˝ enyi graphs and small-world graphs, and a ´ real-world dataset of online blogs. We show that for each case, the proposed sampling theory achieves perfect recovery with high probability. Finally, we apply the proposed sampling theory to semi-supervised classification of online blogs and digit images, where we achieve similar or better performance with fewer labeled samples compared to the previous work.
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RWTH Publications (RWTH Aachen)
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Guillermo Ortiz Jimenez · 2018
In this era of data deluge, we are overwhelmed with massive volumes of extremely complex datasets. Data generated today is complex because it lacks a clear geometric structure, comes in great volumes, and it often contains information from multiple domains. In this thesis, we address these issues and propose two theoretical frameworks to handle such multidomain dataset. To begin with, we extend the recently developed geometric deep learning framework to multidomain graph signals, e.g., time-varying signals, defining a new type of convolutional layer that will allow us to deal with graph signals defined on top of several domains, e.g., electroencephalograms or traffic networks. After discussing its properties and motivating its use, we show how this operation can be efficiently implemented to run on a GPU and demonstrate its generalization abilities on a synthetic dataset. Next, we consider the problem of designing sparse sampling strategies for multidomain signals, which can be represented using tensors. To keep the framework general, we do not restrict ourselves to multidomain signals defined on irregular domains. Nonetheless, this particularization to multidomain graph signals is also presented. To do so, we leverage the multidomain structure of tensor signals and propose to acquire samples using a Kronecker-structured sensing function, thereby circumventing the curse of dimensionality. For designing such sensing functions, we develop several low-complexity greedy algorithms based on submodular optimization methods that compute near-optimal sampling sets. To validate the developed theory, we present several numerical examples, ranging from multi-antenna communications to graph signal processing.
Cited by 1
Armin Eftekhari, Justin Romberg, Senior Member et al. · 2013
Abstract—In this paper, we study a simple correlation-based strategy for estimating the unknown delay and amplitude of a signal based on a small number of noisy, randomly chosen frequency-domain samples. We model the output of this “compressive matched filter ” as a random process whose mean equals the scaled, shifted autocorrelation function of the template signal. Using tools from the theory of empirical processes, we prove that the expected maximum deviation of this process from its mean decreases sharply as the number of measurements increases, and we also derive a probabilistic tail bound on the maximum deviation. Putting all of this together, we bound the minimum number of measurements required to guarantee that the empirical maximum of this random process occurs sufficiently close to the true peak of its mean function. We conclude that for broad classes of signals, this compressive matched filter will successfully estimate the unknown delay (with high probability and within a prescribed tolerance) using a number of random frequency-domain samples that scales inversely with the signal-to-noise ratio and only logarithmically in the observation bandwidth and the possible range of delays. Index Terms—Compressive sensing (CS), matched filtering, random processes, tone estimation.
Cited by 0
Ortiz Jimenez, Guillermo (author) · Research Repository (Delft University of Technology) · 2018
In this era of data deluge, we are overwhelmed with massive volumes of extremely complex datasets. Data generated today is complex because it lacks a clear geometric structure, comes in great volumes, and it often contains information from multiple domains. In this thesis, we address these issues and propose two theoretical frameworks to handle such multidomain dataset.<br/><br/>To begin with, we extend the recently developed geometric deep learning framework to multidomain graph signals, e.g., time-varying signals, defining a new type of convolutional layer that will allow us to deal with graph signals defined on top of several domains, e.g., electroencephalograms or traffic networks. After discussing its properties and motivating its use, we show how this operation can be efficiently implemented to run on a GPU and demonstrate its generalization abilities on a synthetic dataset.<br/><br/>Next, we consider the problem of designing sparse sampling strategies for multidomain signals, which can be represented using tensors. To keep the framework general, we do not restrict ourselves to multidomain signals defined on irregular domains. Nonetheless, this particularization to multidomain graph signals is also presented. To do so, we leverage the multidomain structure of tensor signals and propose to acquire samples using a Kronecker-structured sensing function, thereby circumventing the curse of dimensionality. For designing such sensing functions, we develop several low-complexity greedy algorithms based on submodular optimization methods that compute near-optimal sampling sets. To validate the developed theory, we present several numerical examples, ranging from multi-antenna communications to graph signal processing.
Cited by 0Open access
Arie Feuer, Graham C. Goodwin · Birkhäuser Boston eBooks · 1996
Undoubtably one of the key factors influencing recent technology has been the advent of high speed computational tools. Virtually every advanced engi neering system we come in contact with these days
Cited by 200Open access
Laurent Fesquet, Bruno Torrésani · SPIRE - Sciences Po Institutional REpository · 2011
International audience
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Qiong Wu, Qilian Liang · 2013
Estimating the spectrogram of non-stationary signal relates to many important applications in radar signal processing. In recent years, coprime sampling and array attract attention for their potential of sparse sensing with derivative to estimate autocorrelation coefficients with all lags, which could in turn calculate the power spectrum density. But this theoretical merit is based on the premise that the input signals are wide-sense stationary. In this paper, we take the first step to design coprime sampling algorithm using with non-stationary signal and discuss how to attain the benefits of coprime sampling meanwhile limiting the disadvantages due to lack of observations for estimations.
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Derrick, Timothy R. · Iowa State University Digital Repository (Iowa State University) · 2014
A signal is a time or space varying quantity that conveys information. It may take the form of a sound wave, a voltage, a current, a light wave, a magnetic field, a displacement, a velocity, an acceleration or a host of other physical quantities. These are examples of continuous signals (the signal is present at all instances of time or space). As a matter of convenience we often convert continuous signals into discrete signals by sampling the phenomena at intervals (Figure 3.1).
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J. Y. Shi, José M. F. Moura · 2024
The classic DSP sampling property: “(Uniform) sampling of a bandlimited signal leads to (perfect) replication in the spectral domain.” does not hold in the vertex Graph Signal Processing (GSP) model. Sampling uniformly in GSP does not lead to perfect replicas, but rather distorted replicas [1]. In [2], we introduced a Step L-Step 2 Companion Model Method, S2CM<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>, as a way to introduce new GSP concepts. The GSP companion model is closest to the DSP time model (with different boundary conditions), making it easier to extend DSP concepts. In this paper, we consider GSP sampling in the companion model. We show that GSP sampling theory in the companion model is similar to DSP sampling theory by illustrating the four sampling steps: Subsampling, Decimation, Upsampling, Interpolation, in the companion model.
Cited by 2
Károly Molnár, László Sujbert, Gábor Péceli · 2009
Abstract – In distributed signal processing systems, every node samples analog signals by its own AD converter. Sampling is controlled by autonomous clocks, that are generally not synchronizable. In order to ensure synchronized operation among the different nodes of the distributed system, both the drift of these clocks, and the jitter of the sampling must be handled. This problem is investigated in this paper, and signal processing methods are proposed to guarantee the synchronized operation and to reduce the effect of the jitter. The proposed solution is based on low-level interpolation and resampling of the sampled signals. A realization of this method is demonstrated on a test-system.
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Babazadeh Eslamlou, Gita · reposiTUm (TU Wien) · 2020
The amounts of data collected by automated software and hardware in various domains, such as social networks, bioinformatics and wireless sensor networks, are exploding. Beside the sheer volume of these data-sets also the high velocity (rate of generation) and their variety (data composed of mixture of audio video text, only partially labeled) pose big challenges on their processing. A particular useful methodology to cope with big data is provided by graph signal processing (GSP), which models data-sets as signals defined over large graphs (complex networks). The usage of graph models within GSP entails efficient distributed message passing algorithms that are well suited to deal with large volumes of high-speed data. Moreover, graphs allow to organize heterogeneous data by exploiting application specific notions of similarity, thereby addressing the variety of big data. A key problem studied in GSP is the recovery of a graph signal from its noisy samples at few selected nodes. This problem is relevant, e.g., for semi-supervised learning over graphs, where only few training examples (represented by graph nodes) are labeled and most examples are unlabeled. The problem of determining the labels for the unlabeled data is precisely a graph signal recovery problem. The recovery is feasible for the graph signals which are smooth with respect to the graph. In this work, we investigate the problem of recovering a graph signal from the noisy samples observed at a small number of randomly selected nodes. The signal recovery is formulated as a convex optimization problem. Our approaches exploit the smoothness of typical graph signals occurring in many applications, such as wireless sensor networks or social network analysis. The graph signals are smooth in the sense that the neighboring nodes have similar signal values. In particular, we propose various graph signal recovery methods, which are shown to be particularly well suited for smooth graph signal recovery. Besides, in this dissertation we present a novel and flexible sampling method for signals that are supported on either directed or undirected graphs. The proposed sampling algorithm selects the optimal sampling set from the set of arbitrary weighted graph signal, for any predefined sampling rate, such that the reconstruction (recovery) quality is as high as possible. The algorithm is able to be adaptively adjusted based on the structure of the underlying graph and signal model such as nodes degree and smoothness. The effectiveness of the proposed recovery and sampling methods is verified by numerical experiments on various random graphs along with a real-world data-set. Numerical evaluations show that the proposed algorithms render a highly efficient performance compared to the state-of-the-art methods.
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Lorenzo Laneve · arXiv (Cornell University) · 2023
Quantum Signal Processing (QSP) is a technique that can be used to implement a polynomial transformation $P(x)$ applied to the eigenvalues of a unitary $U$, essentially implementing the operation $P(U)$, provided that $P$ satisfies some conditions that are easy to satisfy. A rich class of previously known quantum algorithms were shown to be derived or reduced to this technique or one of its extensions. In this work, we show that QSP can be used to tackle a new problem, which we call phase extraction, and that this can be used to provide quantum speed-up for proportional sampling, a problem of interest in machine-learning applications and quantum state preparation. We show that, for certain sampling distributions, our algorithm provides an almost-quadratic speed-up over classical sampling procedures. Then we extend the result by constructing a sequence of algorithms that increasingly relax the dependence on the space of elements to sample.
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Holger Boche, Ullrich J. Mönich · mediaTUM – the media and publications repository of the Technical University Munich (Technical University Munich) · 2014
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.
Cited by 6Open access
Rongli Liu, Jianrong Lu, Jinli Ding et al. · 2011
The output signal of charge coupled device (CCD) includes many kinds of noises. So in CCD signal acquisition system, it is a key technique that the CCD signal noises must be eliminated or weakened. The paper analyzes the generated mechanism of CCD signal noises, and designs signal processing circuits based on correlated double sampling (CDS) technique improving the signal-to noise ratio.
Cited by 6