Discrete-time Signals Research Articles

Choi–Williams distribution in linear canonical domains and its application in noisy LFM signals detection

Due to the requirement of signal representation’s flexibility for strong noise interference in non-stationary signal processing, the traditional Choi–Williams distribution (CWD) is extended to the linear canonical domain by using a well-established closed-form instantaneous cross-correlation function (CICF) type of linear canonical transform (LCT) free parameters embedded approach. The derived CICF type of CWD (CICFCWD) unifies all of the linear canonical Choi–Williams distributions, and can be considered as the CWD’s closed-form representation in linear canonical domains. The CICFCWD of a discrete-time signal defined by the sampling equation is discussed for the requirement of digital signal analysis and processing. To break through the limitation that the existing research techniques are limited to quantitative analysis based on numerical simulations, a qualitative analysis to output signal-to-noise ratio (SNR) inequality between the traditional CWD and the CICFCWD for a general noisy signal is introduced, including the inequality modeling and solving. Within this output SNR improvement analysis framework, the strategies on determination LCT free parameters for linear frequency-modulated (LFM) signals added with white noise are developed. Numerical experiments are also carried out to validate the correctness of LCT free parameters selection results and the feasibility of output SNR improvement analysis approach.

Centralized, distributed and sequential fusion estimation from uncertain outputs with correlation between sensor noises and signal

ABSTRACTThis paper focuses on the least-squares linear fusion filter design for discrete-time stochastic signals from multisensor measurements perturbed not only by additive noise, but also by different uncertainties that can be comprehensively modeled by random parameter matrices. The additive noises from the different sensors are assumed to be cross-correlated at the same time step and correlated with the signal at the same and subsequent time steps. A covariance-based approach is used to derive easily implementable recursive filtering algorithms under the centralized, distributed and sequential fusion architectures. Although centralized and sequential estimators both have the same accuracy, the evaluation of their computational complexity reveals that the sequential filter can provide a significant reduction of computational cost over the centralized one. The accuracy of the proposed fusion filters is explored by a simulation example, where observation matrices with random parameters are used to describe different kinds of sensor uncertainties.

A HIDDEN MARKOV MODEL APPROACH TO CHARACTERIZING THE PHOTO-SWITCHING BEHAVIOR OF FLUOROPHORES.

Fluorescing molecules (fluorophores) that stochastically switch between photon-emitting and dark states underpin some of the most celebrated advancements in super-resolution microscopy. While this stochastic behavior has been heavily exploited, full characterization of the underlying models can potentially drive forward further imaging methodologies. Under the assumption that fluorophores move between fluorescing and dark states as continuous time Markov processes, the goal is to use a sequence of images to select a model and estimate the transition rates. We use a hidden Markov model to relate the observed discrete time signal to the hidden continuous time process. With imaging involving several repeat exposures of the fluorophore, we show the observed signal depends on both the current and past states of the hidden process, producing emission probabilities that depend on the transition rate parameters to be estimated. To tackle this unusual coupling of the transition and emission probabilities, we conceive transmission (transition-emission) matrices that capture all dependencies of the model. We provide a scheme of computing these matrices and adapt the forward-backward algorithm to compute a likelihood which is readily optimized to provide rate estimates. When confronted with several model proposals, combining this procedure with the Bayesian Information Criterion provides accurate model selection.

Parameter estimation of discrete-time sinusoidal signals: A nonlinear control approach

This paper considers a parameter estimation problem for discrete-time sinusoidal signals in the presence of measurement noise. Different from most of existing methods, we shall solve the problem based on nonlinear control theory. Specifically, we introduce a constructive nonlinear estimator that enables us to prove an interesting input/output stability property from measurement noise to estimation error. To show efficacy of the proposed method, we also present several numerical examples using different types of signals and noises.

Above the Nyquist Rate, Modulo Folding Does Not Hurt

We consider the problem of recovering a continuous-time bandlimited signal from the discrete-time signal obtained from sampling it every $T_s$ seconds and reducing the result modulo $\Delta$, for some $\Delta>0$. For $\Delta=\infty$ the celebrated Shannon-Nyquist sampling theorem guarantees that perfect recovery is possible provided that the sampling rate $1/T_s$ exceeds the so-called Nyquist rate. Recent work by Bhandari et al. has shown that for any $\Delta>0$ perfect reconstruction is still possible if the sampling rate exceeds the Nyquist rate by a factor of $\pi e$. In this letter we improve upon this result and show that for finite energy signals, perfect recovery is possible for any $\Delta>0$ and any sampling rate above the Nyquist rate. Thus, modulo folding does not degrade the signal, provided that the sampling rate exceeds the Nyquist rate. This claim is proved by establishing a connection between the recovery problem of a discrete-time signal from its modulo reduced version and the problem of predicting the next sample of a discrete-time signal from its past, and leveraging the fact that for a bandlimited signal the prediction error can be made arbitrarily small.

Lattice Functions for the Analysis of Analog-to-Digital Conversion

Analog-to-digital (A/D) converters are the common interface between analog signals and the domain of digital discrete-time signal processing. In essence, this domain simultaneously incorporates quantization both in amplitude and time, i.e. amplitude quantization and uniform time sampling. Thus, we view A/D conversion as a sampling process in both the time and amplitude domains based on the observation that the underlying continuous-time signals representing digital sequences can be sampled in a lattice---i.e. at points restricted to lie on a uniform grid both in time and amplitude. We refer to them as lattice functions. This is in contrast with the traditional approach based on the classical sampling theorem and quantization error analysis. The latter has been mainly addressed with the help of probabilistic models, or deterministic ones either confined to very particular scenarios or considering worst-case assumptions. In this paper, we provide a deterministic theoretical analysis and framework for the functions involved in digital discrete-time processing. We show that lattice functions possess a rich analytic structure in the context of integral-valued entire functions of exponential type. We derive set and spectral properties of this class of functions. This allows us to prove in a deterministic way and for general bandlimited functions a fundamental lower bound on the maximum frequency component introduced by quantization that is independent of the resolution of the quantizer.

Covariance-Based Estimation for Clustered Sensor Networks Subject to Random Deception Attacks.

In this paper, a cluster-based approach is used to address the distributed fusion estimation problem (filtering and fixed-point smoothing) for discrete-time stochastic signals in the presence of random deception attacks. At each sampling time, measured outputs of the signal are provided by a networked system, whose sensors are grouped into clusters. Each cluster is connected to a local processor which gathers the measured outputs of its sensors and, in turn, the local processors of all clusters are connected with a global fusion center. The proposed cluster-based fusion estimation structure involves two stages. First, every single sensor in a cluster transmits its observations to the corresponding local processor, where least-squares local estimators are designed by an innovation approach. During this transmission, deception attacks to the sensor measurements may be randomly launched by an adversary, with known probabilities of success that may be different at each sensor. In the second stage, the local estimators are sent to the fusion center, where they are combined to generate the proposed fusion estimators. The covariance-based design of the distributed fusion filtering and fixed-point smoothing algorithms does not require full knowledge of the signal evolution model, but only the first and second order moments of the processes involved in the observation model. Simulations are provided to illustrate the theoretical results and analyze the effect of the attack success probability on the estimation performance.

Lattices sampling and sampling rate conversion of multidimensional bandlimited signals in the linear canonical transform domain

The linear canonical transform (LCT) has been shown to be a powerful tool for optics and signal processing. Many theories for this transform are already known, but the uniform sampling theorem, as well as the sampling rate conversion theory about arbitrary lattices sampling in the LCT domain are still to be determined. Focusing on these issues, this paper carefully investigates arbitrary lattices sampling, the sampling with separable matrices and nonseparable matrices, to obtain uniform sampling theorem and the sampling rate conversion theory in the LCT domain. Firstly, the spectral expression of the discrete-time signal sampled via arbitrary lattice is deduced in the LCT domain. Based on it we propose the alias-free sampling relationship between two matrices and present the perfect reconstruction expressions for bandlimited signals in the LCT domain. Secondly, for further research on discrete signals to obtain sampling rate conversion theory, we define the multidimensional discrete time linear canonical transform (MDTLCT), as well as the convolution for the MDTLCT. Thirdly, the formulas of multidimensional interpolation and decimation via integer matrices in the LCT domain are derived. Then, based on the results of interpolation and decimation, we make analyses of the sampling rate conversion via rational matrices in the LCT domain, including spectral analyses and the formulas in time domain. Finally, simulation results and the potential applications of the theories are also presented.

A novel VLSI design of radix-4 DFT in current mode

ABSTRACTDiscrete-time Fourier transform (DFT) is viewed as an important tool in discrete time signal processing. Applications in wireless communication such as OFDM uses DFT/IDFT in its receiver and transmitter. For small battery powered wireless devices, discrete time analogue DFT can be very useful as a low-energy front-end. The quest for a reduction in the effect due to the mismatch of transistors lead to higher radix structure. It becomes very challenging for the designer to build an analogue circuit for implementation of DFT with radix sizes 4, 8, and so on. This is mainly because of hand calculation of circuit-level equations from butterfly algorithm becomes a long process. Thus, a design methodology becomes a necessary option in this regard. Here an algorithm is proposed for the generation of circuit-level equations leading to signal routing table for the circuit of basic radix-4 FFT. Following that algorithm, a current mode all analogue circuit with cascode current mirror is proposed. Simulations are carried out in SPICE using BSIM4 65 nm CMOS process. A mismatch noise model is also made to show the reduction in error with higher radix structure. The non-ideal effects due to mismatch in Vth are analysed through Monte-Carlo simulation.

Empirical Mode Decomposition in Discrete Time Signals Denoising

Abstract This study explores the data-driven properties of the empirical mode decomposition (EMD) for signal denoising. EMD is an acknowledged procedure which has been widely used for non-stationary and nonlinear signal processing. The main idea of the EMD method is to decompose the analyzed signal into components without using expansion functions. This is a signal dependent representation and provides intrinsic mode functions (IMFs) as components. These are analyzed, through their Hurst exponent and if they are found being noisy components they will be partially or integrally eliminated. This study presents an EMD decomposition-based filtering procedure applied to test signals, the results are evaluated through signal to noise ratio (SNR) and mean square error (MSE). The obtained results are compared with discrete wavelet transform based filtering results.

Pulse Oximeter for Low SpO2 Level Detection Using Discrete Time Signal Processing Algorithm

Abstract Oximeter is an important clinical device used for measuring peripheral capillary oxygen saturation (SpO2) in blood and hence accurate results are needed in order to help physicians predict clinical problems in the initial stage(s) of liver or kidney diagnosis. Different issues associated with the accuracy of SpO2 and heart rate measurement accuracy are studied in this work. With the understanding of these issues, a new SpO2 monitoring system is proposed that comprises of a better detection method, novel discrete time signal processing (DTSP) algorithm, and a custom-made oximeter probe head. The proposed SpO2 measurement system is capable of determining low levels of SpO2 present in human blood and produce the results in a short time that enable real-time monitoring of a patient SpO2. It can also distinguish low level of SpO2 against background noise.

On recovery of discrete time signals from their periodic subsequences

The paper investigates recoverability of discrete time signals (sequences) from their subsequences sampled at m-periodic points. It is shown that this recoverability is associated with arbitrarily small spectrum degeneracy of subsequences amended via insertion of dummy elements and bundled into a system. It appears that, for a given m, the signals of a general kind can be approximated by signals with this feature. A recovery algorithm is suggested, and some robustness of this recovery is established.

Decimations of intrinsic mode functions via semi-infinite programming based optimal adaptive nonuniform filter bank design approach

Abstract A signal can be represented as the sum of the intrinsic mode functions via performing the empirical mode decomposition. For the discrete time signals, the lengths of the intrinsic mode functions are equal to the lengths of the input signals. As there is usually more than one intrinsic mode function, the total numbers of discrete points of all the intrinsic mode functions are usually more than the lengths of the input signals. In other words, the empirical mode decomposition is an oversampled representation. For some applications such as the compression application, the oversampled representation is not preferred. Therefore, this paper proposes an optimal adaptive nonuniform filter bank design approach for performing the decimations on the intrinsic mode functions. In particular, the passbands of the intrinsic mode functions are estimated based on an adaptive gradient algorithm. Then, the intrinsic mode functions are nonuniformly downsampled and upsampled with the sampling integers derived based on their estimated passbands. Next, a bank of filters is employed to reconstruct the original signal. Here, the passbands of the filters are also derived based on those of the intrinsic mode functions. After that, the nonuniform filter bank design problem is formulated as a semi-infinite programming problem such that the total ripple energies of all the filters are minimized subject to the specifications on the absolute maximum values of both the real part and the imaginary part of the reconstruction error. The semi-infinite programming problem is approximated by a semi-definite programming problem. Computer numerical simulation results show that our proposed system could achieve a very small reconstruction error at a very small oversampling ratio.

Enhancing teager energy operator based on a novel and appealing concept: Signal mass

In analogy with a spring-mass system, the original Teager Energy Operator (T) approximately models the energy of a discrete-time signal (x[·]) as the squared product of its amplitude (A) by its instantaneous frequency (Ω). Interestingly, this article shows that not only the mechanical entity but also x[·] has a mass (η) expressing the resistance in changing the signal amplitude over time. In addition, T is modified based on η so that A2·Ω2 is computed exactly in terms of x[·], creating an enhanced energy operator (T) which allows for more precise analyses in contrast to those provided by the original tool. Lastly, illustrative examples are included to reassure the applicability of the proposed approach.

Implementation of Encryption Algorithm and Wireless Image Transmission System on FPGA

In this paper, we proposed to improve bit insertion based on the common chaotic encryption algorithm, which reduces the computational complexity of the chaotic encryption algorithm and is used on low computational systems. We changed the encryption steps from permutation to XOR and XOR to bit insertion, which is our proposed bitwise operation based on encryption. Next, we proposed a four-dimensional chaotic system using the discrete time signal of the chaotic system for the key generator and optimized the floating point operation as well as FPGA resources of the chaotic system. Then, we implemented the algorithm on our Nios II-based wireless image transmission system, where the system's processor clock is 50 MHz. Finally, we performed a security analysis on our encryption algorithm, and the results show that our proposed algorithm consumes less computing resources while maintaining sufficient security.

An Optimized Sensorless Charge Balance Controller Based on a Damped Current Model for Flyback Converter Operating in DCM

This paper presents an Optimized Sensorless Charge Balance (OSCB) controller based on a damped current model for flyback converter operating in Discontinuous Conduction Mode (DCM). By solving total differential equations of non-ideal transformer currents, the damped current model is derived with consideration of parasitics, leakage inductance of transformer, and the Resistor-Capacitor-Diode (RCD) snubber circuit. Based on the proposed model, current observation and control algorithms of the Sensorless Charge Balance (SCB) controller are optimized, which forms the OSCB control strategy. The average current damping is considered in the equivalent discrete-time small signal model. Furthermore, frequency analyses show that OSCB controller achieves higher closed-loop bandwidth and lower overshoot than a SCB controller, which indicates an improved transient performance. Finally, both OSCB and conventional SCB controllers are experimentally evaluated on a flyback converter prototype.

Centralized filtering and smoothing algorithms from outputs with random parameter matrices transmitted through uncertain communication channels

The least-squares linear centralized estimation problem is addressed for discrete-time signals from measured outputs whose disturbances are modeled by random parameter matrices and correlated noises. These measurements, coming from different sensors, are sent to a processing center to obtain the estimators and, due to random transmission failures, some of the data packet processed for the estimation may either contain only noise (uncertain observations), be delayed (sensor delays) or even be definitely lost (packet dropouts). Different sequences of Bernoulli random variables with known probabilities are employed to describe the multiple random transmission uncertainties of the different sensors. Using the last observation that successfully arrived when a packet is lost, the optimal linear centralized fusion estimators, including filter, multi-step predictors and fixed-point smoothers, are obtained via an innovation approach; this approach is a general and useful tool to find easily implementable recursive algorithms for the optimal linear estimators under the least-squares optimality criterion. The proposed algorithms are obtained without requiring the evolution model of the signal process, but using only the first and second-order moments of the processes involved in the measurement model.

On an Application of the Absolute Stability Theory to Sampled-Data Stabilization

A nonlinear Lur’e-type plant with a sector bound nonlinearity is considered. The plant is stabilized by a discrete-time feedback signal with a nonperiodic uncertain sampling. The sampling control function is nonlinear and also obeys some sectoral constraints at discrete (sampling) times. The linear matrix inequality (LMI) conditions for the stability of the closed-loop system are obtained.

A Novel Method of Discrete-Time Signal Amplification Using NEMS Devices

In this paper we propose a novel method of realizing discrete-time (D-T) signal amplification using Nano-Electro-Mechanical (NEMS) devices. The amplifier uses mechanical devices instead of traditional solid-state circuits. The proposed NEMS-based D-T amplifier provides high gain and operate on a wide dynamic range of signals, consuming only a few micro watts of power. The proposed concept is subsequently verified using Verilog-A model of the NEMS device. Modifications in the proposed amplifier to suit different specifications are also presented.

Robust Detection of Extreme Events Using Twitter: Worldwide Earthquake Monitoring

Timely detection and accurate description of extreme events, such as natural disasters and other crisis situations, are crucial for emergency management and mitigation. Extreme-event detection is challenging, since one has to rely upon reports from human observers appointed to specific geographical areas, or on an expensive and sophisticated infrastructure. In the case of earthquakes, geographically dense sensor networks are expensive to deploy and maintain. Therefore, only some regions—or even countries—are able to acquire useful information about the effects of earthquakes in their own territory. An inexpensive and viable alternative to this problem is to detect extreme real-world events through people's reactions in online social networks. In particular, Twitter has gained popularity within the scientific community for providing access to real-time “citizen sensor” activity. Nevertheless, the massive amount of messages in the Twitter stream, along with the noise it contains, underpin a number of difficulties when it comes to Twitter-based event detection. We contribute to address these challenges by proposing an online method for detecting unusual bursts in discrete-time signals extracted from Twitter. This method only requires a one-off semisupervised initialization and can be scaled to track multiple signals in a robust manner. We also show empirically how our proposed approach, which was envisioned for generic event detection, can be adapted for worldwide earthquake detection, where we compare the proposed model to the state of the art for earthquake tracking using social media. Experimental results validate our approach as a competitive alternative in terms of precision and recall to leading solutions, with the advantage of implementation simplicity and worldwide scalability.