scholarly journals On the Rate-Distortion Function of Sampled Cyclostationary Gaussian Processes

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 345
Author(s):  
Emeka Abakasanga ◽  
Nir Shlezinger ◽  
Ron Dabora
Keyword(s):  
Sampling Rate ◽  
Rate Distortion ◽  
Sampling Interval ◽  
Distortion Function ◽  
Wide Sense ◽  
Information Theoretic ◽  
Synchronous Sampling ◽  
Asynchronous Sampling ◽  
Two Parameters ◽  
The Relationship

Man-made communications signals are typically modelled as continuous-time (CT) wide-sense cyclostationary (WSCS) processes. As modern processing is digital, it is applied to discrete-time (DT) processes obtained by sampling the CT processes. When sampling is applied to a CT WSCS process, the statistics of the resulting DT process depends on the relationship between the sampling interval and the period of the statistics of the CT process: When these two parameters have a common integer factor, then the DT process is WSCS. This situation is referred to as synchronous sampling. When this is not the case, which is referred to as asynchronous sampling, the resulting DT process is wide-sense almost cyclostationary (WSACS). The sampled CT processes are commonly encoded using a source code to facilitate storage or transmission over wireless networks, e.g., using compress-and-forward relaying. In this work, we study the fundamental tradeoff between rate and distortion for source codes applied to sampled CT WSCS processes, characterized via the rate-distortion function (RDF). We note that while RDF characterization for the case of synchronous sampling directly follows from classic information-theoretic tools utilizing ergodicity and the law of large numbers, when sampling is asynchronous, the resulting process is not information stable. In such cases, the commonly used information-theoretic tools are inapplicable to RDF analysis, which poses a major challenge. Using the information-spectrum framework, we show that the RDF for asynchronous sampling in the low distortion regime can be expressed as the limit superior of a sequence of RDFs in which each element corresponds to the RDF of a synchronously sampled WSCS process (yet their limit is not guaranteed to exist). The resulting characterization allows us to introduce novel insights on the relationship between sampling synchronization and the RDF. For example, we demonstrate that, differently from stationary processes, small differences in the sampling rate and the sampling time offset can notably affect the RDF of sampled CT WSCS processes.

scholarly journals Rate Distortion Function of Gaussian Asymptotically WSS Vector Processes

Entropy ◽  
2018 ◽  
Vol 20 (9) ◽  
pp. 719 ◽  
Author(s):  
Jesús Gutiérrez-Gutiérrez ◽  
Marta Zárraga-Rodríguez ◽  
Pedro Crespo ◽  
Xabier Insausti
Keyword(s):  
Integral Formula ◽  
Moving Average ◽  
Rate Distortion ◽  
Distortion Function ◽  
Wide Sense ◽  
Vector Process

In this paper, we obtain an integral formula for the rate distortion function (RDF) of any Gaussian asymptotically wide sense stationary (AWSS) vector process. Applying this result, we also obtain an integral formula for the RDF of Gaussian moving average (MA) vector processes and of Gaussian autoregressive MA (ARMA) AWSS vector processes.

scholarly journals Low-Complexity Rate-Distortion Optimization of Sampling Rate and Bit-Depth for Compressed Sensing of Images

Entropy ◽  
2020 ◽  
Vol 22 (1) ◽  
pp. 125
Author(s):  
Qunlin Chen ◽  
Derong Chen ◽  
Jiulu Gong ◽  
Jie Ruan
Keyword(s):  
Compressed Sensing ◽  
Signal To Noise Ratio ◽  
Sampling Rate ◽  
Rate Distortion ◽  
Image Transmission ◽  
Low Complexity ◽  
Rate Model ◽  
Bit Rate ◽  
Compression Performance ◽  
The Relationship

Compressed sensing (CS) offers a framework for image acquisition, which has excellent potential in image sampling and compression applications due to the sub-Nyquist sampling rate and low complexity. In engineering practices, the resulting CS samples are quantized by finite bits for transmission. In circumstances where the bit budget for image transmission is constrained, knowing how to choose the sampling rate and the number of bits per measurement (bit-depth) is essential for the quality of CS reconstruction. In this paper, we first present a bit-rate model that considers the compression performance of CS, quantification, and entropy coder. The bit-rate model reveals the relationship between bit rate, sampling rate, and bit-depth. Then, we propose a relative peak signal-to-noise ratio (PSNR) model for evaluating distortion, which reveals the relationship between relative PSNR, sampling rate, and bit-depth. Finally, the optimal sampling rate and bit-depth are determined based on the rate-distortion (RD) criteria with the bit-rate model and the relative PSNR model. The experimental results show that the actual bit rate obtained by the optimized sampling rate and bit-depth is very close to the target bit rate. Compared with the traditional CS coding method with a fixed sampling rate, the proposed method provides better rate-distortion performance, and the additional calculation amount amounts to less than 1%.

Exergy analysis of a turboprop engine at different flight altitude and speeds using novel consideration

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ali Dinc ◽  
Yousef Gharbia
Keyword(s):  
Fuel Consumption ◽  
Thermal Efficiency ◽  
Exergy Efficiency ◽  
Specific Fuel Consumption ◽  
Flight Altitude ◽  
Fuel Flow ◽  
Turboprop Engine ◽  
Shaft Power ◽  
Two Parameters ◽  
The Relationship

Abstract In this study, exergy efficiency calculations of a turboprop engine were performed together with main performance parameters such as shaft power, specific fuel consumption, fuel flow, thermal efficiency etc., for a range of flight altitude (0–14 km) and flight speeds (0–0.6 Mach). A novel exergy efficiency formula was derived in terms of specific fuel consumption and it is shown that these two parameters are inversely proportional to each other. Moreover, a novel exergy efficiency and thermal efficiency relation was also derived. The relationship showed that these two parameters are linearly proportional to each other. Exergy efficiency of the turboprop engine was found to be in the range of 23–33%. Thermal efficiency of the turboprop engine was found to be around 25–35%. Exergy efficiency is higher at higher speeds and altitude where the specific fuel consumption is lower. Conversely, exergy efficiency of the engine is lower for lower speeds and altitude where the specific fuel consumption is higher.

scholarly journals Area Entropy and Quantized Mass of Black Holes from Information Theory

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 858
Author(s):  
Dongshan He ◽  
Qingyu Cai
Keyword(s):  
Information Theory ◽  
Black Hole ◽  
Black Hole Entropy ◽  
Quantum Corrections ◽  
Compton Wavelength ◽  
Information Theoretic ◽  
Curved Space ◽  
Thermodynamic Entropy ◽  
Hole Area ◽  
The Relationship

In this paper, we present a derivation of the black hole area entropy with the relationship between entropy and information. The curved space of a black hole allows objects to be imaged in the same way as camera lenses. The maximal information that a black hole can gain is limited by both the Compton wavelength of the object and the diameter of the black hole. When an object falls into a black hole, its information disappears due to the no-hair theorem, and the entropy of the black hole increases correspondingly. The area entropy of a black hole can thus be obtained, which indicates that the Bekenstein–Hawking entropy is information entropy rather than thermodynamic entropy. The quantum corrections of black hole entropy are also obtained according to the limit of Compton wavelength of the captured particles, which makes the mass of a black hole naturally quantized. Our work provides an information-theoretic perspective for understanding the nature of black hole entropy.

scholarly journals Cerebral CT Perfusion in Acute Stroke: The Effect of Lowering the Tube Load and Sampling Rate on the Reproducibility of Parametric Maps

Diagnostics ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 1121
Author(s):  
Georgios S. Ioannidis ◽  
Søren Christensen ◽  
Katerina Nikiforaki ◽  
Eleftherios Trivizakis ◽  
Kostas Perisinakis ◽  
...  
Keyword(s):  
Cerebral Blood Volume ◽  
Ct Perfusion ◽  
Sampling Rate ◽  
Volumetric Analysis ◽  
Sampling Interval ◽  
Diagnostic Efficiency ◽  
Temporal Sampling ◽  
Sampling Intervals ◽  
The Mean ◽  
Parametric Maps

The aim of this study was to define lower dose parameters (tube load and temporal sampling) for CT perfusion that still preserve the diagnostic efficiency of the derived parametric maps. Ninety stroke CT examinations from four clinical sites with 1 s temporal sampling and a range of tube loads (mAs) (100–180) were studied. Realistic CT noise was retrospectively added to simulate a CT perfusion protocol, with a maximum reduction of 40% tube load (mAs) combined with increased sampling intervals (up to 3 s). Perfusion maps from the original and simulated protocols were compared by: (a) similarity using a voxel-wise Pearson’s correlation coefficient r with in-house software; (b) volumetric analysis of the infarcted and hypoperfused volumes using commercial software. Pearson’s r values varied for the different perfusion metrics from 0.1 to 0.85. The mean slope of increase and cerebral blood volume present the highest r values, remaining consistently above 0.7 for all protocol versions with 2 s sampling interval. Reduction of the sampling rate from 2 s to 1 s had only modest impacts on a TMAX volume of 0.4 mL (IQR −1–3) (p = 0.04) and core volume of −1.1 mL (IQR −4–0) (p < 0.001), indicating dose savings of 50%, with no practical loss of diagnostic accuracy. The lowest possible dose protocol was 2 s temporal sampling and a tube load of 100 mAs.

scholarly journals Calculating the Number of Cluster Heads Based on the Rate-Distortion Function in Wireless Sensor Networks

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Mingxin Yang ◽  
Jingsha He ◽  
Yuqiang Zhang
Keyword(s):  
Wireless Sensor Networks ◽  
Energy Consumption ◽  
Sensor Networks ◽  
Data Fusion ◽  
Rate Distortion ◽  
Distortion Function ◽  
Sensor Nodes ◽  
Wireless Sensor ◽  
Wireless Sensor Nodes ◽  
Cluster Heads

Due to limited resources in wireless sensor nodes, energy efficiency is considered as one of the primary constraints in the design of the topology of wireless sensor networks (WSNs). Since data that are collected by wireless sensor nodes exhibit the characteristics of temporal association, data fusion has also become a very important means of reducing network traffic as well as eliminating data redundancy as far as data transmission is concerned. Another reason for data fusion is that, in many applications, only some of the data that are collected can meet the requirements of the sink node. In this paper, we propose a method to calculate the number of cluster heads or data aggregators during data fusion based on the rate-distortion function. In our discussion, we will first establish an energy consumption model and then describe a method for calculating the number of cluster heads from the point of view of reducing energy consumption. We will also show through theoretical analysis and experimentation that the network topology design based on the rate-distortion function is indeed more energy-efficient.

scholarly journals On the complexity of assimilation in urban communities

2021 ◽  
Vol 6 (1) ◽  
Author(s):  
Renita Murimi
Keyword(s):  
Complex Systems ◽  
Urban Communities ◽  
Human Experience ◽  
Urban Environments ◽  
Urban Systems ◽  
Sociological Perspective ◽  
Information Theoretic ◽  
Information Theoretic Measures ◽  
Urban Complex ◽  
The Relationship

AbstractCities are microcosms representing a diversity of human experience. The complexity of urban systems arises from this diversity, where the services that cities offer to their inhabitants have to be tailored for their unique requirements. This paper studies the complexity of urban environments in terms of the assimilation of its communities. We examine the urban assimilation complexity with respect to the foreignness between communities and formalize the level of complexity using information-theoretic measures. Our findings contribute to a sociological perspective of the relationship between urban complex systems and the diversity of communities that make up urban systems.

Derivation Mathematical Equations for Future Calculation of Potential Evapotranspiration in Iraq, A Review of Application of Thornthwaite Evapotranspiration

2019 ◽  
Vol 60 (5) ◽  
pp. 1037-1048
Author(s):  
Hussein Ilaibi Zamil Al-Sudani
Keyword(s):  
Water Balance ◽  
Potential Evapotranspiration ◽  
Coefficient Of Determination ◽  
Research Review ◽  
Climate Conditions ◽  
Average Temperature ◽  
Mean Temperature ◽  
Mathematical Equations ◽  
Two Parameters ◽  
The Relationship

     In any natural area or water body, evapotranspiration is one of the important outcomes in the water balance equation. As a significant method and depending on monthly average temperature, estimating of potential Evapotranspiration depending on Thornthwaite method was adopted in this research review. Estimate and discuss evapotranspiration by using Thornthwaite method is the main objectives of this research review with considerable details as well as compute potential evapotranspiration based on climatologically data obtained in Iraq. Temperature - evapotranspiration relationship can be estimated between those two parameters to reduce cost and time and facilitate calculation of water balance in lakes, river, and hydrogeological basins. The relationship was obtained using Thornthwaite method in Iraq by dividing the area into seven sectors according to geographic latitude. Each sector has multi meteorological stations where thirty two stations were used with different periods of records. A mathematical relationship was obtained between mean temperature and corrected potential evapotranspiration with (97.45) to (99.84) coefficient of determination. The mean temperature has a decreasing pattern from southern east towards northern west of Iraq affected by Mediterranean Sea climate conditions, while corrected potential evapotranspiration has the opposite direction regarding increased value because of a direct relationship with temperature.

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