scholarly journals Fourier analysis: the simplification of a complex waveform into simple component sine waves of different amplitudes and frequencies

2020 ◽  
pp. S102-S103
Author(s):  
AI Mamoojee
Keyword(s):  
Fourier Analysis ◽  
Fundamental Frequency ◽  
Simple Wave ◽  
Sine Wave ◽  
Frequency Wave ◽  
Invasive Blood Pressure ◽  
Time Frequency ◽  
Simple Component ◽  
Electrocardiogram Ecg ◽  
Electroencephalogram Eeg

Fourier analysis is the simplification of a complex waveform into simple component sine waves of different amplitudes and frequencies. A discussion on Fourier analysis necessitates reiteration of the physics of waves. A wave is a series of repeating disturbances that propagate in space and time. Frequency: the number of oscillations, or cycles per second. It is measured in Hertz and denoted as 1/time or s-1. Fundamental frequency: the lowest frequency wave in a series. It is also known as the first harmonic. Every other wave in the series is an exact multiple of the fundamental frequency. Harmonic: whole number multiples of the fundamental frequency. Amplitude: the maximum disturbance or displacement from zero caused by the wave. This is the height of the wave. Period: time to complete one oscillation. Wavelength: physical length of one complete cycle. This can be between two crests or two troughs. The higher the frequency, the shorter the wavelength. Velocity: frequency x wavelength. Phase: displacement of one wave compared to another, described as 0°–360°. A sine wave is a simple wave. It can be depicted as the path of a point travelling round a circle at a constant speed, defined by the equation ‘y = sinx’. Combining sine waves of different frequency, amplitude and phase can yield any waveform, and, conversely, any wave can be simplified into its component sine waves. Fourier analysis is a mathematical method of analysing a complex periodic waveform to find its constituent frequencies (as sine waves). Complex waveforms can be analysed, with very simple results. Usually, few sine and cosine waves combine to create reasonably accurate representations of most waves. Fourier analysis finds its anaesthetic applications in invasive blood pressure, electrocardiogram (ECG) and electroencephalogram (EEG) signals, which are all periodic waveforms. It enables monitors to display accurate representations of these biological waveforms. Fourier analysis was developed by Joseph Fourier, a mathematician who analysed and altered periodic waveforms. It is done by computer programmes that plot the results of the analysis as a spectrum of frequencies with amplitude on the y-axis and frequency on the x-axis.

Information-based analysis of the coupling between brain and heart reactions to olfactory stimulation

2021 ◽  
pp. 1-11
Author(s):  
Najmeh Pakniyat ◽  
Mohammad Hossein Babini ◽  
Vladimir V. Kulish ◽  
Hamidreza Namazi
Keyword(s):  
Time Series ◽  
Biomedical Science ◽  
Strongly Correlated ◽  
Eeg Signals ◽  
Ecg Signals ◽  
Olfactory Stimuli ◽  
Electrocardiogram Ecg ◽  
First Time ◽  
Electroencephalogram Eeg ◽  
The Brain

BACKGROUND: Analysis of the heart activity is one of the important areas of research in biomedical science and engineering. For this purpose, scientists analyze the activity of the heart in various conditions. Since the brain controls the heart’s activity, a relationship should exist among their activities. OBJECTIVE: In this research, for the first time the coupling between heart and brain activities was analyzed by information-based analysis. METHODS: Considering Shannon entropy as the indicator of the information of a system, we recorded electroencephalogram (EEG) and electrocardiogram (ECG) signals of 13 participants (7 M, 6 F, 18–22 years old) in different external stimulations (using pineapple, banana, vanilla, and lemon flavors as olfactory stimuli) and evaluated how the information of EEG signals and R-R time series (as heart rate variability (HRV)) are linked. RESULTS: The results indicate that the changes in the information of the R-R time series and EEG signals are strongly correlated (ρ=-0.9566). CONCLUSION: We conclude that heart and brain activities are related.

scholarly journals Second-Order Nonlinearity in Triangular Lattice Perforated Gold Film due to Surface Plasmas Resonance

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Renlong Zhou ◽  
Xiaoshuang Chen ◽  
Yingyi Xiao ◽  
Bingju Zhou ◽  
Lingxi Wu ◽  
...  
Keyword(s):  
Fundamental Frequency ◽  
Triangular Lattice ◽  
Gold Film ◽  
Second Harmonic ◽  
Resonance Effect ◽  
Second Order ◽  
Square Lattice ◽  
Frequency Wave ◽  
Surface Plasmas ◽  
Second Order Nonlinearity

We have studied the excitation second-order nonlinearity through a triangular lattice perforated gold film instead of square lattice in many papers. Under the excitation of surface plasmas resonance effect, the second order nonlinearity exists in the noncentrosymmetric split-ring resonators arrays. Reflection of fundamental frequency wave through a triangular lattice perforated gold film is obtained. We also described the second harmonic conversion efficiencies in the second order nonlinear optical process with the spectra. Moreover, the electric field distributions of fundamental frequency above the gold film region are calculated. The light propagation through the holes results in the enhancement of the second order nonlinearity including second harmonic generation as well as the sum (difference) frequency generation.

Understanding the nonlinear behavior of EEG with advanced machine learning in artifact elimination

2021 ◽  
Author(s):  
Md Samiul Haque Sunny ◽  
Shifat Hossain ◽  
Nashrah Afroze ◽  
Md. Kamrul Hasan ◽  
Eklas Hossain ◽  
...  
Keyword(s):  
Nonlinear Behavior ◽  
Cognitive Status ◽  
Brain Diseases ◽  
Eeg Signal ◽  
Hilbert Huang Transform ◽  
Neuro Fuzzy ◽  
Research Goal ◽  
Adaptive Noise ◽  
Electrocardiogram Ecg ◽  
Electroencephalogram Eeg

Abstract Steady-state Visually Evoked Potential (SSVEP) based Electroencephalogram (EEG) signal is utilized in brain-computer interface paradigms, diagnosis of brain diseases, and measurement of the cognitive status of the human brain. However, various artifacts such as the Electrocardiogram (ECG), Electrooculogram (EOG), and Electromyogram (EMG) are present in the raw EEG signal, which adversely affect the EEG-based appliances. In this research, Adaptive Neuro-fuzzy Interface Systems (ANFIS) and Hilbert-Huang Transform (HHT) are primarily employed to remove the artifacts from EEG signals. This work proposes Adaptive Noise Cancellation (ANC) and ANFIS based methods for canceling EEG artifacts. A mathematical model of EEG with the aforementioned artifacts is determined to accomplish the research goal, and then those artifacts are eliminated based on their mathematical characteristics. ANC, ANFIS, and HHT algorithms are simulated on the MATLAB platform, and their performances are also justified by various error estimation criteria using hardware implementation.

Epileptic Seizure-Induced Hypoxemia in Infants with Apparent Life-Threatening Events

PEDIATRICS ◽  
1994 ◽  
Vol 94 (2) ◽  
pp. 148-156
Author(s):  
John Hewertson ◽  
Martin P. Samuels ◽  
David P. Southall ◽  
Christian F. Poets ◽  
Stewart G. Boyd ◽  
...  
Keyword(s):  
Median Duration ◽  
Epileptic Seizure ◽  
Sinus Tachycardia ◽  
Partial Seizures ◽  
Severe Hypoxemia ◽  
Life Threatening ◽  
Electrocardiogram Ecg ◽  
Electroencephalogram Eeg ◽  
Normal Standard ◽  
Median Interval

Objective. To describe the physiologic changes that occur during epileptic seizure (ES)-induced apparent life-threatening events (ALTE) and to provide an explanation for the mechanism whereby the hypoxemia characterizing these events occurred. Patients and design. Six infants were retrospectively selected from a group of 17 because they had ALTE documented on physiologic recordings where the first change in signals was in the electroencephalogram (EEG). The 17 infants had clinical features suggestive of partial seizures (but normal standard EEGs) and were from a sample of 172 infants with recurrent ALTE. All 17 infants underwent continuous recordings of breathing, electrocardiogram (ECG), oxygenation, and EEG, but only in 6 was an ES-induced ALTE recorded and the physiologic changes described. Results. Twenty-three ALTE were documented in six infants. Events commenced with an abnormality in the EEG, followed by a decrease in SaO2 after a median interval of 27 seconds (range 2 to 147). Despite resuscitation, the median duration of severe hypoxemia (SaO2 ≤60%) was 40 seconds (range 8 to 74). In 18 events (five infants) there was a median of four apneic pauses (range 1 to 9) preceding the decrease in SaO2 by a median duration of 24 seconds (range 3 to 48). The longest apneic pause per event lasted a median of 19 seconds (range 8 to 47). Breathing movements continued in five events (four infants), and expiratory airflow in one. Sinus tachycardia was found in 19 of the 23 events (six infants), but there were no cardiac arrhythmias. Conclusions. ES in infants can manifest as ALTE and be accompanied by potentially life-threatening episodes of severe hypoxemia and apnea, despite a normal EEG between events.

Nonlinear Approach to Brain Signal Modeling

2011 ◽  
pp. 2834-2839
Author(s):  
Tugce Balli ◽  
Ramaswamy Palaniappan
Keyword(s):  
Signal Processing ◽  
Electrical Activity ◽  
Nonlinear Modeling ◽  
Biological Mechanisms ◽  
Linear Modeling ◽  
Memory Impairments ◽  
Biological Signal ◽  
Biological Signals ◽  
Electrocardiogram Ecg ◽  
Electroencephalogram Eeg

Biological signal is a common term used for time series measurements that are obtained from biological mechanisms and basically represent some form of energy produced by the biological mechanisms. Examples of such signals are electroencephalogram (EEG), which is the electrical activity of brain recorded by electrodes placed on the scalp; electrocardiogram (ECG), which is electrical activity of heart recorded from chest, and electromyogram (EMG), which is recorded from skin as electrical activity generated by skeletal muscles (Akay, 2000). Nowadays, biological signals such as EEG and ECG are analysed extensively for diagnosing conditions like cardiac arrhythmias in the case of ECG and epilepsy, memory impairments, and sleep disorders in case of EEG. Apart from clinical diagnostic purposes, in recent years there have been many developments for utilising EEG for brain computer interface (BCI) designs (Vaughan & Wolpaw, 2006). The field of signal processing provides many methods for analysis of biological signals. One of the most important steps in biological signal processing is the extraction of features from the signals. The assessment of such information can give further insights to the functioning of the biological system. The selection of proper methods and algorithms for feature extraction (i.e., linear/nonlinear methods) are current challenges in the design and application of real time biological signal analysis systems. Traditionally, linear methods are used for the analysis of biological signals (mostly in analysis of EEG). Although the conventional linear analysis methods simplify the implementation, they can only give an approximation to the underlying properties of the signal when the signal is in fact nonlinear. Because of this, there has been an increasing interest for utilising nonlinear analysis techniques in order to obtain a better characterisation of the biological signals. This chapter will lay the backgrounds to linear and nonlinear modeling of EEG signals, and propose a novel nonlinear model based on exponential autoregressive (EAR) process, which proves to be superior to conventional linear modeling techniques.

Experimental Study of Time-Frequency Effect of Rocks

2012 ◽  
Vol 204-208 ◽  
pp. 755-760
Author(s):  
Xin Lin Wan ◽  
Su Zhang
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Sine Wave ◽  
Intersection Point ◽  
Frequency Effect ◽  
Nonlinear Frequency ◽  
Time Frequency ◽  
Physical Mechanisms ◽  
Nonlinear Frequency Response ◽  
Water Saturated

Sine wave loading experiments are carried out on MTS for pump-oil saturated Nanjing sandstones and water saturated Dali marbles. The Young’s modulus and velocities of longitudinal wave and transverse wave increase with the frequency, and there are notable dispersions. The existence of micro defects in saturated rocks result in hysteresis at the sinusoidal loading experiments. The variation curves of instantaneous Young’s modulus with stress for loading and unloading intersect, and an “X” shape figure is obtained. As the frequency of the sinusoidal wave increases, the position of the intersection point moves to higher modulus area. Thus the modulus dispersion increases. Some physical mechanisms of nonlinear frequency response of rock are revealed. The results obtained are very important for nonlinear wave study, and the theoretical study and application of earthquake and engineering.

Time-frequency analysis of heart rate variability using short-time Fourier analysis

2000 ◽  
Vol 21 (2) ◽  
pp. 229-240 ◽  
Author(s):  
Sigrid Elsenbruch ◽  
Zhishun Wang ◽  
William C Orr ◽  
J D Z Chen
Keyword(s):  
Heart Rate ◽  
Heart Rate Variability ◽  
Fourier Analysis ◽  
Frequency Analysis ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Short Time

scholarly journals Active vibrissal sensing in rodents and marsupials

2011 ◽  
Vol 366 (1581) ◽  
pp. 3037-3048 ◽  
Author(s):  
Ben Mitchinson ◽  
Robyn A. Grant ◽  
Kendra Arkley ◽  
Vladan Rankov ◽  
Igor Perkon ◽  
...  
Keyword(s):  
Fourier Analysis ◽  
Active Control ◽  
Fundamental Frequency ◽  
Horizontal Plane ◽  
Second Harmonic ◽  
Early Stage ◽  
Monodelphis Domestica ◽  
Head Turning ◽  
Previous Evidence ◽  
Mystacial Vibrissae

In rats, the long facial whiskers (mystacial macrovibrissae) are repetitively and rapidly swept back and forth during exploration in a behaviour known as ‘whisking’. In this paper, we summarize previous evidence from rats, and present new data for rat, mouse and the marsupial grey short-tailed opossum ( Monodelphis domestica ) showing that whisking in all three species is actively controlled both with respect to movement of the animal's body and relative to environmental structure. Using automatic whisker tracking, and Fourier analysis, we first show that the whisking motion of the mystacial vibrissae, in the horizontal plane, can be approximated as a blend of two sinusoids at the fundamental frequency (mean 8.5, 11.3 and 7.3 Hz in rat, mouse and opossum, respectively) and its second harmonic. The oscillation at the second harmonic is particularly strong in mouse (around 22 Hz) consistent with previous reports of fast whisking in that species. In all three species, we found evidence of asymmetric whisking during head turning and following unilateral object contacts consistent with active control of whisker movement. We propose that the presence of active vibrissal touch in both rodents and marsupials suggests that this behavioural capacity emerged at an early stage in the evolution of therian mammals.

Measurement of Low-Frequency Wave Propagation in a Railway Contact Wire with Dispersive Characteristics Using Wavelet Transform

2006 ◽  
Vol 321-323 ◽  
pp. 1609-1615 ◽  
Author(s):  
Sung Yong Park ◽  
Byung Uk Jeon ◽  
Jang Moo Lee ◽  
Yong Hyeon Cho
Keyword(s):  
Wave Propagation ◽  
Wavelet Transform ◽  
Propagation Velocity ◽  
Beam Model ◽  
Wave Propagation Velocity ◽  
Essential Information ◽  
Frequency Wave ◽  
Contact Wire ◽  
Time Frequency ◽  
Cross Correlation Analysis

The railway contact wire, which supplies electric railways with electric power, plays an important role in determining the maximum railway velocity. In general, the maximum allowable velocity of an electric railway is less than seventy percent of the wave propagation velocity of the contact wire. Because the contact wire is more a beam model with dispersive wave characteristics than a string model, the wave propagation velocity depends on the frequency. For this reason, there have been only few studies on the wave propagation of the contact wire. In this paper, we proposed two useful methods for estimating the wave propagation velocity of the railway contact wire by using the Gabor wavelet transform on the experimental signals. In the first method, the ridges of wavelet transform, which contain the essential information about dispersive characteristics, are used. Specifically, the wave propagation velocity of the contact wire can be extracted from the time difference of the wavelet ridges of the measured signals. In the second method, the cross-correlation analysis of each wavelet transform is used to extract the wave propagation. The selection of the optimal Gabor shaping factor for the best time-frequency localization by using the Shannon entropy cost function is also discussed.

BCI-Touch Based System: A Multimodal CAD Interface for Object Manipulation

2013 ◽  
Author(s):  
Rohit Bhat ◽  
Akshay Deshpande ◽  
Rahul Rai ◽  
Ehsan Tarkesh Esfahani
Keyword(s):  
Computer Aided Design ◽  
Brain Activity ◽  
Temporal Cortex ◽  
Target Object ◽  
Time Frequency ◽  
System A ◽  
Computer Interfaces ◽  
Brain Signals ◽  
Aided Design ◽  
Electroencephalogram Eeg

The aim of this paper is to explore a new multimodal Computer Aided Design (CAD) platform based on brain-computer interfaces and touch based systems. The paper describes experiments and algorithms for manipulating geometrical objects in CAD systems using touch-based gestures and movement imagery detected though brain waves. Gestures associated with touch based systems are subjected to ambiguity since they are two dimensional in nature. Brain signals are considered here as the main source to resolve these ambiguities. The brainwaves are recorded in terms of electroencephalogram (EEG) signals. Users wear a neuroheadset and try to move and rotate a target object on a touch screen. As they perform these actions, the EEG headset collects brain activity from 14 locations on the scalp. The data is analyzed in the time-frequency domain to detect the desynchronizations of certain frequency bands (3–7Hz, 8–13 Hz, 14–20Hz 21–29Hz and 30–50Hz) in the temporal cortex as an indication of motor imagery.

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