HEART MURMURS DETECTION AND CHARACTERIZATION USING WAVELET ANALYSIS WITH RENYI ENTROPY

2017 ◽  
Vol 17 (06) ◽  
pp. 1750093 ◽  
Author(s):  
BOUTANA DAOUD ◽  
KOURAS NAYAD ◽  
BARKAT BRAHAM ◽  
BENIDIR MESSAOUD
Keyword(s):  
Aortic Stenosis ◽  
Heart Diseases ◽  
Pulmonary Stenosis ◽  
Peak Frequency ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Discrete Wavelet ◽  
Time Duration ◽  
Time Frequency ◽  
Main Components

Phonocardiogram signals (PCGs) represent a nonstationary signal due to their complicated production. Also, during the registration they may be added with different noise and pathological murmurs. Indeed, in real situation, the heart sound signal (HSs) may present some abnormal murmur characterizing a variety of heart diseases. This work deals with the segmentation of pathological PCGs based on the Discrete Wavelet Transform (DWT) which permits signal decomposition in different frequency bands. After the decomposition step, we estimate the Renyi Entropy (RE) of the detail coefficients. Then, we apply a threshold allowing detecting the murmur of the PCGs. After the detection, we characterize the results in time–frequency domain in order to extract some features such as frequency band, peak frequency and time duration of the abnormal murmur. The validation of the method is evaluated and proved using some pathological PCGs such as: Early Aortic Stenosis (EAS), Late Aortic Stenosis (LAS), Mitral Regurgitation (MR), Aortic Regurgitation (AR), Opening Snap (OS) and Pulmonary Stenosis (PS). The method presents good results in terms of the detection and the characterization of the main components and the abnormal murmurs associated with some valves disease.

Improved Characterization of GNSS Jammers Using Short-Term Time-Frequency Rényi Entropy

2018 ◽  
Vol 54 (4) ◽  
pp. 1918-1930 ◽  
Author(s):  
Pai Wang ◽  
Ediz Cetin ◽  
Andrew G. Dempster ◽  
Yongqing Wang ◽  
Siliang Wu
Keyword(s):  
Renyi Entropy ◽  
Rényi Entropy ◽  
Short Term ◽  
Time Frequency

scholarly journals Rule-Based EEG Classifier Utilizing Local Entropy of Time–Frequency Distributions

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 451
Author(s):  
Jonatan Lerga ◽  
Nicoletta Saulig ◽  
Ljubiša Stanković ◽  
Damir Seršić
Keyword(s):  
Virtual Instrument ◽  
Diagnostic Techniques ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Separation Procedure ◽  
Eeg Analysis ◽  
Frequency Distributions ◽  
Time Frequency ◽  
Multicomponent Signals ◽  
Challenging Tasks

Electroencephalogram (EEG) signals are known to contain signatures of stimuli that induce brain activities. However, detecting these signatures to classify captured EEG waveforms is one of the most challenging tasks of EEG analysis. This paper proposes a novel time–frequency-based method for EEG analysis and characterization implemented in a computer-aided decision-support system that can be used to assist medical experts in interpreting EEG patterns. The computerized method utilizes EEG spectral non-stationarity, which is clearly revealed in the time–frequency distributions (TFDs) of multicomponent signals. The proposed algorithm, which is based on the modification of the Rényi entropy, called local or short-term Rényi entropy (STRE), was upgraded with a blind component separation procedure and instantaneous frequency (IF) estimation. The method was applied to EEGs of both forward and backward movements of the left and right hands, as well as to EEGs of imagined hand movements, which were captured by a 19-channel EEG recording system. The obtained results show that in a given virtual instrument, the proposed methods efficiently distinguish between real and imagined limb movements by considering their signatures in terms of the dominant EEG component’s IFs at the specified subset of EEG channels (namely, F3, F4, F7, F8, T3, and T4). Furthermore, computing the number of EEG signal components, their extraction, and IF estimation provide important information that shows potential to enhance existing clinical diagnostic techniques for detecting the intensity, location, and type of brain function abnormalities in patients with neurological motor control disorders.

scholarly journals Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory. Part I. Single-particle states

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Jiaju Zhang ◽  
M.A. Rajabpour
Keyword(s):  
Excited States ◽  
Single Particle ◽  
Renyi Entropy ◽  
Rényi Entropy ◽  
Large Momentum ◽  
Particle State ◽  
Two Dimensional ◽  
Universal Form ◽  
Conformal Field ◽  
Harmonic Chain

Abstract We investigate the Rényi entropy of the excited states produced by the current and its derivatives in the two-dimensional free massless non-compact bosonic theory, which is a two-dimensional conformal field theory. We also study the subsystem Schatten distance between these states. The two-dimensional free massless non-compact bosonic theory is the continuum limit of the finite periodic gapless harmonic chains with the local interactions. We identify the excited states produced by current and its derivatives in the massless bosonic theory as the single-particle excited states in the gapless harmonic chain. We calculate analytically the second Rényi entropy and the second Schatten distance in the massless bosonic theory. We then use the wave functions of the excited states and calculate the second Rényi entropy and the second Schatten distance in the gapless limit of the harmonic chain, which match perfectly with the analytical results in the massless bosonic theory. We verify that in the large momentum limit the single-particle state Rényi entropy takes a universal form. We also show that in the limit of large momenta and large momentum difference the subsystem Schatten distance takes a universal form but it is replaced by a new corrected form when the momentum difference is small. Finally we also comment on the mutual Rényi entropy of two disjoint intervals in the excited states of the two-dimensional free non-compact bosonic theory.

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