scholarly journals Lack of the Lower Bound for the Shannon Entropy

2021 ◽  
pp. 1-4
Author(s):  
J. Ladvánszky Ladvánszky
Keyword(s):  
Lower Bound ◽  
Shannon Entropy ◽  
Basic Characteristic ◽  
Arbitrary Order ◽  
Signal To Noise Ratio ◽  
Point Of View ◽  
Signal To Noise ◽  
Theoretical Limit ◽  
Qam Modulation ◽  
Energetic Point

Shannon entropy is a basic characteristic of communications from the energetic point of view. Despite this fact, an expression for entropy as a function of the signal-to-noise ratio is still missing. In this paper, that shortage has been corrected first. Using that expression, lower bound for entropy has been investigated. We prove that such finite nonzero bound does not exist, therefore there is no theoretical limit for reduction of the effect of noise. The proof is valid for QAM modulation of arbitrary order.

scholarly journals There is no Theoretical Limit for Noise Reduction in Digital Communications

2021 ◽  
Vol 6 (1) ◽  
pp. 34
Author(s):  
János Ladvánszky
Keyword(s):  
Noise Reduction ◽  
Shannon Entropy ◽  
Signal To Noise Ratio ◽  
Point Of View ◽  
Signal To Noise ◽  
Theoretical Limit ◽  
Successful Communication ◽  
Index Terms ◽  
Noise Ratio ◽  
Energetic Point

Shannon entropy is a basic characteristic of communications from energetic point of view. Entropy has been expressed as a function of signal to noise ratio, and lower bound for entropy has been investigated. We prove that finite nonzero bound does not exist, therefore in case of M-QAM modulation, there is no theoretical limit for reduction of the effect of noise. In our investigations, averaging is considered, exploiting the zero expected value of the Gaussian noise. Index Terms—Shannon entropy, probability of successful communication, bit error rate, signal to noise ratio, bound for noise reduction.

Coupled Granular/Continuous Media – Results and Challenges

MRS Advances ◽  
2017 ◽  
Vol 2 (49) ◽  
pp. 2661-2668
Author(s):  
Horia Gavrila ◽  
Doina Elena Gavrila
Keyword(s):  
Thermal Stability ◽  
Grain Size ◽  
Magnetic Recording ◽  
Granular Media ◽  
Signal To Noise Ratio ◽  
Signal To Noise ◽  
Theoretical Limit ◽  
Perpendicular Recording ◽  
Perpendicular Magnetic Recording ◽  
Longitudinal Recording

ABSTRACTWhile the most promising longitudinal recording systems cannot surpass the theoretical limit of about 200 Gb/in2 for areal recording density and the demand for higher densities is permanently increasing, the perpendicular magnetic recording constitutes the realistic issue to the longitudinal one. The perpendicular magnetic recording offers significant advantages, the most important being stronger write and read fields, and therefore the use of media of higher anisotropy, smaller grain size, higher signal-to-noise ratio, and a better thermal stability. Unfortunately, the perpendicular recording has to cope some important physical and technological difficulties. To overcome them, many ingenious solutions were proposed. In this paper the coupled granular/continuous (CGC) media, a subtle association of the continuous and, respectively, granular media, are analysed from the viewpoint of their magnetic and recording properties. The challenges and possible improvements of CGC media are discussed.

STOCHASTIC RESONANCE IN CHUA’S CIRCUIT DRIVEN BY AMPLITUDE OR FREQUENCY MODULATED SIGNALS

1994 ◽  
Vol 04 (02) ◽  
pp. 441-446 ◽  
Author(s):  
V.S. ANISHCHENKO ◽  
M.A. SAFONOVA ◽  
L.O. CHUA
Keyword(s):  
Numerical Simulation ◽  
Stochastic Resonance ◽  
Signal To Noise Ratio ◽  
Point Of View ◽  
Chua’S Circuit ◽  
Signal Distortion ◽  
Signal To Noise ◽  
Chua's Circuit ◽  
Noise Ratio ◽  
Modulated Signals

Using numerical simulation, we establish the possibility of realizing the stochastic resonance (SR) phenomenon in Chua’s circuit when it is excited by either an amplitude-modulated or a frequency-modulated signal. It is shown that the application of a frequency-modulated signal to a Chua’s circuit operating in a regime of dynamical intermittency is preferable over an amplitude-modulated signal from the point of view of minimizing the signal distortion and maximizing the signal-to-noise ratio (SNR).

scholarly journals NOISE STABILITY OF SIGNAL RECEPTION ALGORITHMS WITH MULTIPULSE PULSE-POSITION MODULATION

2018 ◽  
Vol 42 (1) ◽  
pp. 167-174 ◽  
Author(s):  
V. I. Parfenov ◽  
D. Y. Golovanov
Keyword(s):  
Communication Systems ◽  
Pulse Sequence ◽  
Signal To Noise Ratio ◽  
Point Of View ◽  
Estimation Accuracy ◽  
Pulse Position Modulation ◽  
Signal To Noise ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Noise Ratio

An algorithm for estimating time positions and amplitudes of a periodic pulse sequence from a small number of samples was proposed. The number of these samples was determined only by the number of pulses. The performance of this algorithm was considered on the assumption that the spectrum of the original signal is limited with an ideal low-pass filter or the Nyquist filter, and conditions for the conversion from one filter to the other were determined. The efficiency of the proposed algorithm was investigated through analyzing in which way the dispersion of estimates of time positions and amplitudes depends on the signal-to-noise ratio and on the number of pulses in the sequence. It was shown that, from this point of view, the efficiency of the algorithm decreases with increasing number of sequence pulses. Besides, the efficiency of the proposed algorithm decreases with decreasing signal-to-noise ratio.It was found that, unlike the classical maximum likelihood algorithm, the proposed algorithm does not require a search for the maximum of a multivariable function, meanwhile characteristics of the estimates are practically the same for both these methods. Also, it was shown that the estimation accuracy of the proposed algorithm can be increased by an insignificant increase in the number of signal samples.The results obtained may be used in the practical design of laser communication systems, in which the multipulse pulse-position modulation is used for message transmission. 

scholarly journals Collecting Microplastics in Gardens: Case Study (i) of Soil

2021 ◽  
Vol 9 ◽  
Author(s):  
Zahra Sobhani ◽  
Yunlong Luo ◽  
Christopher T. Gibson ◽  
Youhong Tang ◽  
Ravi Naidu ◽  
...  
Keyword(s):  
Signal To Noise Ratio ◽  
Point Of View ◽  
Signal To Noise ◽  
Statistical Point ◽  
Image Mapping ◽  
Noise Ratio ◽  
In The Beginning ◽  
Raman Image ◽  
Selection Of

As an emerging contaminant, microplastic is receiving increasing attention. However, the contamination source is not fully known, and new sources are still being identified. Herewith, we report that microplastics can be found in our gardens, either due to the wrongdoing of leaving plastic bubble wraps to be mixed with mulches or due to the use of plastic landscape fabrics in the mulch bed. In the beginning, they were of large sizes, such as > 5 mm. However, after 7 years in the garden, owing to natural degradation, weathering, or abrasion, microplastics are released. We categorize the plastic fragments into different groups, 5 mm–0.75 mm, 0.75 mm–100 μm, and 100–0.8 μm, using filters such as kitchenware, meaning we can collect microplastics in our gardens by ourselves. We then characterized the plastics using Raman image mapping and a logic-based algorithm to increase the signal-to-noise ratio and the image certainty. This is because the signal-to-noise ratio from a single Raman spectrum, or even from an individual peak, is significantly less than that from a spectrum matrix of Raman mapping (such as 1 vs. 50 × 50) that contains 2,500 spectra, from the statistical point of view. From the 10 g soil we sampled, we could detect the microplastics, including large (5 mm–100 μm) fragments and small (<100 μm) ones, suggesting the degradation fate of plastics in the gardens. Overall, these results warn us that we must be careful when we do gardening, including selection of plastic items for gardens.

scholarly journals An Algorithm for Automatic Recogniton of Digital QAM Modulations

2019 ◽  
Vol 25 (3) ◽  
pp. 36-41
Author(s):  
Alexandru-Daniel Luţă ◽  
Paul Bechet
Keyword(s):  
Lower Order ◽  
Signal To Noise Ratio ◽  
Recognition Rate ◽  
Automatic Recognition ◽  
Signal To Noise ◽  
Small Influence ◽  
Qam Modulation ◽  
Digital Modulations ◽  
Simulation Results ◽  
Noise Ratio

Abstract This paper proposes a new Matlab-developed algorithm for automatic recognition of digital modulations using the constellation of states. Using this technique the automatic distinction between four digital modulation schemes (8-QAM, 16-QAM, 32-QAM and 64-QAM) was made. It has been seen that the efficiency of the algorithm is influenced by the type of modulation, the value of the signal-to-noise ratio and the number of samples. In the case of an AWGN noise channel the simulation results indicated that the value of SNR (signal-to-noise ratio) has a small influence on the recognition rate for lower-order QAM (8-QAM and 16-QAM). The length of the signal may change essentially the recognition rate of this algorithm especially for modulations with a high number of bits per symbol. Consequently, for the 64-QAM modulation in a case of 25dB signal-to-noise ratio the recognition rate is doubled if the sample rate is incresed from 5400 to 80640.

Low-Frequency Scanning Capacitance Microscopy

1997 ◽  
Vol 500 ◽  
Author(s):  
Š. Lányi ◽  
M. Hruškovic
Keyword(s):  
Signal To Noise Ratio ◽  
Low Frequency ◽  
Point Of View ◽  
Dielectric Losses ◽  
Frequency Range ◽  
Signal To Noise ◽  
Input Stage ◽  
Frequency Scanning ◽  
Noise Ratio ◽  
Parallel Conductance

ABSTRACTThe operation principle and main properties of a Scanning Capacitance Microscope (SCM) are described. It is called low-frequency, because in its design typical low-frequency techniques are utilised. The main attention is focused on its lateral resolution, signal-to-noise ratio and the possibility to detect dielectric losses.Mapping the electrostatic field of a shielded microscope probe was used to calculate the stray capacitance, flux density, sensitivity and contrast obtained on a flat conducting surface, as well as on a surface covered by a thin dielectric film. The effect of dielectric losses, represented by a parallel conductance, on the detected capacitance and the resulting phase shift has been derived.Using the results of mapping, the requirements on a SCM input stage and the possible solutions are discussed. From the point of view of frequency range and noise the best is an electrometric input stage, with input impedance represented by its capacitance.The achieved signal-to-noise ratio of the low frequency Scanning Capacitance Microscope renders the extension of the working frequency range to lower frequencies. The input stage can be optimised for a frequency range from about 1 kHz to a few MHz, with the possibility to extend it to about 10 MHz at the cost of reduced sensitivity at the lowest frequencies.

SYMBOL RATE. ESTIMATION BOUNDS

2021 ◽  
Author(s):  
Е.А. БРУСИН
Keyword(s):  
Performance Evaluation ◽  
Lower Bound ◽  
Signal To Noise Ratio ◽  
Observation Interval ◽  
Spectral Characteristics ◽  
Interval Duration ◽  
Signal To Noise ◽  
Rate Estimation ◽  
Estimation Performance ◽  
Symbol Rate

В статье обсуждаются проблемы оценивания символьной частоты и определения эффективности получаемых оценок. Предложенный подход позволяет определить границы оценивания символьной частоты для сигналов различных видов модуляции и спектральныххарактеристик. Получено аналитическое выражение для нормированной модифицированной нижней границы Крамера-Рао оценивания символьной частоты для сигналов с косинусным скруглением. Представлены зависимости соответствующих границ от коэффициента скругления, отношения сигнал/шум на символ и длительности интервала наблюдения. The article discusses the problems of symbol rate estimation and the estimation performance evaluation. The proposed approach allows us to determine the symbol rate estimation bounds for signals of various types of modulation and various spectral characteristics. An analytical expression for the symbol rate modified Kramer-Rao lower bound is obtained for signals with root raised cosine spectrum. The dependences of the corresponding boundaries on the roll-off factor, the signal-to-noise ratio per symbol, and the observation interval duration are presented.

scholarly journals The Degradation of Automotive Radar Sensor Signals Caused by Vehicle Vibrations and Other Nonlinear Movements

Sensors ◽  
2020 ◽  
Vol 20 (21) ◽  
pp. 6195
Author(s):  
Florian Hau ◽  
Florian Baumgärtner ◽  
Martin Vossiek
Keyword(s):  
Continuous Wave ◽  
Signal To Noise Ratio ◽  
Linear Acceleration ◽  
Point Of View ◽  
Additional Contribution ◽  
General Description ◽  
Constant False Alarm Rate ◽  
Automotive Radar ◽  
Signal To Noise ◽  
Noise Ratio

As the demands on modern radar systems with respect to accuracy, reliability, and availability increase, a detailed assessment of the influence of nonlinear movements has become necessary. In particular, from the point of view of radar, different types of movements, such as any kind of acceleration, braking situation, or vehicle vibration, are essential parts of any traffic scenario. These unavoidable motions, in which the relative velocity changes within one measurement cycle, are called nonlinear movements. These nonlinearities contribute to intermediate frequencies, which are comparable to the extensively described nonlinearities of a frequency ramp. This additional contribution to the intermediate signal has a direct effect on the signal-to-noise ratio and thus on the accuracy and probability of target detection. This paper presents a study of various types of nonlinear motion and a detailed definition of the resulting parameters based on a variety of vehicle-based measurements. An advanced signal model of frequency-modulated continuous wave (FMCW) radar is introduced and verified in addition to a detailed mathematical description of spectral signal behaviour in sinusoidal motions and linear acceleration. The theoretical and experimental results in idealised point targets are transferred to real complex road users. Furthermore, by applying established automotive signal processing steps in the form of an ordered statistical constant false alarm rate (OS CFAR), the consequences of determining the noise level are also shown. In combination with the already introduced signal behaviour, these results enabled general description of the signal-to-noise ratio of nonlinear movements in complex traffic scenarios.

Artifact Robustness, Inter- and Intraindividual Baseline Stability, and Rational EEG Parameter Selection

2002 ◽  
Vol 96 (1) ◽  
pp. 54-59 ◽  
Author(s):  
Jörgen Bruhn ◽  
Thomas W. Bouillon ◽  
Andreas Hoeft ◽  
Steven L. Shafer
Keyword(s):  
Shannon Entropy ◽  
Signal To Noise Ratio ◽  
Approximate Entropy ◽  
Signal To Noise ◽  
Spectral Edge Frequency ◽  
Spectral Edge ◽  
Median Baseline ◽  
Before And After ◽  
Artifact Rejection ◽  
Noise Ratio

Background Artifact robustness (i.e., size of deviation of an electroencephalographic parameter value from baseline caused by artifacts) and baseline stability (i.e., consistency of median baseline values) of electroencephalographic parameters profoundly influence electroencephalography-based pharmacodynamic parameter estimation and the usefulness of the processed electroencephalogram as measure of the arousal state of the central nervous system (depth of anesthesia). In this study, the authors compared the artifact robustness and the interindividual and intraindividual baseline stability of several univariate descriptors of the electroencephalogram (Shannon entropy, approximate entropy, spectral edge frequency 95, delta ratio, and canonical univariate parameter). Methods Electroencephalographic data of 16 healthy volunteers before and after administration of an intravenous bolus of propofol (2 mg/kg body weight) were analyzed. Each volunteer was studied twice. The baseline electroencephalogram was recorded for a median of 18 min before drug administration. For each electroencephalographic descriptor, the authors calculated the following: (1) baseline variability (= (median baseline - median effect) [i.e., signal]/SD baseline [i.e., noise]) without artifact rejection; (2) baseline variability with artifact rejection; and (3) baseline stability within and between individuals (= (median baseline - median effect) averaged over all volunteers/SD of all median baselines). Results Without artifact rejection, Shannon entropy and canonical univariate parameter displayed the highest signal-to-noise ratio. After artifact rejection, approximate entropy, Shannon entropy, and the canonical univariate parameter displayed the highest signal-to-noise ratio. Baseline stability within and between individuals was highest for approximate entropy. Conclusions With regard to robustness against artifacts, the electroencephalographic entropy parameters and the canonical univariate parameter were superior to spectral edge frequency 95 and delta ratio. Electroencephalographic approximate entropy displayed the best interindividual and intraindividual baseline stability.

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