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Hilbert Spectrum
The Hilbert spectrum (sometimes referred to as the Hilbert amplitude spectrum), named after David Hilbert, is a statistical tool that can help in distinguishing among a mixture of moving signals. The spectrum itself is decomposed into its component sources using independent component analysis. The separation of the combined effects of unidentified sources (blind signal separation) has applications in climatology, seismology, and biomedical imaging. Conceptual summary The Hilbert spectrum is computed by way of a 2-step process consisting of: * Preprocessing a signal separate it into intrinsic mode functions using a mathematical decomposition such as singular value decomposition (SVD) or empirical mode decomposition (EMD); * Applying the Hilbert transform to the results of the above step to obtain the instantaneous frequency spectrum of each of the components. The Hilbert transform defines the imaginary part of the function to make it an analytic function (sometimes referred to ...
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Signal Strength
In telecommunications, particularly in radio frequency engineering, signal strength refers to the transmitter power output as received by a reference antenna at a distance from the transmitting antenna. High-powered transmissions, such as those used in broadcasting, are expressed in dB-millivolts per metre (dBmV/m). For very low-power systems, such as mobile phones, signal strength is usually expressed in dB-microvolts per metre (dBμV/m) or in decibels above a reference level of one milliwatt (dBm). In broadcasting terminology, 1 mV/m is 1000 μV/m or 60 dBμ (often written dBu). ;Examples: *100 dBμ or 100 mV/m: blanketing interference may occur on some receivers *60 dBμ or 1.0 mV/m: frequently considered the edge of a radio station's protected area in North America *40 dBμ or 0.1 mV/m: the minimum strength at which a station can be received with acceptable quality on most receivers Relationship to average radiated power The electric field strength at a specific point ...
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Climatology
Climatology (from Greek , ''klima'', "place, zone"; and , '' -logia'') or climate science is the scientific study of Earth's climate, typically defined as weather conditions averaged over a period of at least 30 years. This modern field of study is regarded as a branch of the atmospheric sciences and a subfield of physical geography, which is one of the Earth sciences. Climatology now includes aspects of oceanography and biogeochemistry. The main methods employed by climatologists are the analysis of observations and modelling of the physical processes that determine the climate. The main topics of research are the study of climate variability, mechanisms of climate changes and modern climate change. Basic knowledge of climate can be used within shorter term weather forecasting, for instance about climatic cycles such as the El Niño–Southern Oscillation (ENSO), the Madden–Julian oscillation (MJO), the North Atlantic oscillation (NAO), the Arctic oscillation (AO), the Pac ...
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Ultrasound
Ultrasound is sound waves with frequency, frequencies higher than the upper audible limit of human hearing range, hearing. Ultrasound is not different from "normal" (audible) sound in its physical properties, except that humans cannot hear it. This limit varies from person to person and is approximately 20 Hertz, kilohertz (20,000 hertz) in healthy young adults. Ultrasound devices operate with frequencies from 20 kHz up to several gigahertz. Ultrasound is used in many different fields. Ultrasonic devices are used to detect objects and measure distances. Ultrasound imaging or sonography is often used in medicine. In the nondestructive testing of products and structures, ultrasound is used to detect invisible flaws. Industrially, ultrasound is used for cleaning, mixing, and accelerating chemical processes. Animals such as bats and porpoises use ultrasound for locating Predation, prey and obstacles. History Acoustics, the science of sound, starts as far back as Pyth ...
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Blood Flow
Hemodynamics or haemodynamics are the dynamics of blood flow. The circulatory system is controlled by homeostatic mechanisms of autoregulation, just as hydraulic circuits are controlled by control systems. The hemodynamic response continuously monitors and adjusts to conditions in the body and its environment. Hemodynamics explains the physical laws that govern the flow of blood in the blood vessels. Blood flow ensures the transportation of nutrients, hormones, metabolic waste products, oxygen, and carbon dioxide throughout the body to maintain cell-level metabolism, the regulation of the pH, osmotic pressure and temperature of the whole body, and the protection from microbial and mechanical harm. Blood is a non-Newtonian fluid, and is most efficiently studied using rheology rather than hydrodynamics. Because blood vessels are not rigid tubes, classic hydrodynamics and fluids mechanics based on the use of classical viscometers are not capable of explaining haemodynamics. The ...
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Richard Cobbold (Scientist)
Richard Cobbold (1797 – 5 January 1877) was a British writer. Life Richard Cobbold was born in 1797 in the Suffolk town of Ipswich, to John (1746–1835) and the poet and writer Elizabeth (née Knipe) Cobbold (1764–1824). The Cobbolds were a large and affluent family who made their money from the brewing industry. Educated at Caius College, Cambridge, Cobbold entered the church, starting at St Mary-le-Tower in Ipswich before moving to Wortham in 1825 with his wife and three sons. He remained there until his death on 5 January 1877. Cobbold is best known as the author of the ''History of Margaret Catchpole'', a novel based on the romantic adventures of a woman living in the neighbourhood of Ipswich, in whom Cobbold's father had taken a kindly interest. For the copyright of this book he is said to have received £1,000. However Cobbold did not make much money by his other literary ventures, which were mostly undertaken for charitable purposes. Thus his account of ''Mar ...
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Instantaneous Phase
Instantaneous phase and frequency are important concepts in signal processing that occur in the context of the representation and analysis of time-varying functions. The instantaneous phase (also known as local phase or simply phase) of a ''complex-valued'' function ''s''(''t''), is the real-valued function: :\varphi(t) = \arg\, where arg is the complex argument function. The instantaneous frequency is the temporal rate of change of the instantaneous phase. And for a ''real-valued'' function ''s''(''t''), it is determined from the function's analytic representation, ''s''a(''t''): :\begin \varphi(t) &= \arg\ \\ pt &= \arg\, \end where \hat(t) represents the Hilbert transform of ''s''(''t''). When ''φ''(''t'') is constrained to its principal value, either the interval or , it is called ''wrapped phase''. Otherwise it is called ''unwrapped phase'', which is a continuous function of argument ''t'', assuming ''s''a(''t'') is a continuous function of ''t''. Unless ot ...
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Hilbert–Huang Transform
The Hilbert–Huang transform (HHT) is a way to decompose a signal into so-called intrinsic mode functions (IMF) along with a trend, and obtain instantaneous frequency data. It is designed to work well for data that is nonstationary and nonlinear. In contrast to other common transforms like the Fourier transform, the HHT is an algorithm that can be applied to a data set, rather than a theoretical tool. The Hilbert–Huang transform (HHT), a NASA designated name, was proposed by Norden E. Huang et al. (1996, 1998, 1999, 2003, 2012). It is the result of the empirical mode decomposition (EMD) and the Hilbert spectral analysis (HSA). The HHT uses the EMD method to decompose a signal into so-called intrinsic mode functions (IMF) with a trend, and applies the HSA method to the IMFs to obtain instantaneous frequency data. Since the signal is decomposed in time domain and the length of the IMFs is the same as the original signal, HHT preserves the characteristics of the varying freque ...
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Frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is equal to one event per second. The period is the interval of time between events, so the period is the reciprocal of the frequency. For example, if a heart beats at a frequency of 120 times a minute (2 hertz), the period, —the interval at which the beats repeat—is half a second (60 seconds divided by 120 beats). Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio signals (sound), radio waves, and light. Definitions and units For cyclical phenomena such as oscillations, waves, or for examples of simple harmonic motion, the term ''frequency'' is defined as the number of cycles or vibrations per unit of time. Th ...
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Time
Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future. It is a component quantity of various measurements used to sequence events, to compare the duration of events or the intervals between them, and to quantify rates of change of quantities in material reality or in the conscious experience. Time is often referred to as a fourth dimension, along with three spatial dimensions. Time has long been an important subject of study in religion, philosophy, and science, but defining it in a manner applicable to all fields without circularity has consistently eluded scholars. Nevertheless, diverse fields such as business, industry, sports, the sciences, and the performing arts all incorporate some notion of time into their respective measuring systems. 108 pages. Time in physics is operationally defined as "what a clock reads". The physical nature of time is addre ...
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Energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light. Energy is a conserved quantity—the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The unit of measurement for energy in the International System of Units (SI) is the joule (J). Common forms of energy include the kinetic energy of a moving object, the potential energy stored by an object (for instance due to its position in a field), the elastic energy stored in a solid object, chemical energy associated with chemical reactions, the radiant energy carried by electromagnetic radiation, and the internal energy contained within a thermodynamic system. All living organisms constantly take in and release energy. Due to mass–energy equivalence, any object that has mass whe ...
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Progressive Function
In mathematics, a progressive function ''ƒ'' ∈ ''L''2(R) is a function whose Fourier transform is supported by positive frequencies only: :\mathop\hat \subseteq \mathbb_+. It is called super regressive if and only if the time reversed function ''f''(−''t'') is progressive, or equivalently, if :\mathop\hat \subseteq \mathbb_-. The complex conjugate of a progressive function is regressive, and vice versa. The space of progressive functions is sometimes denoted H^2_+(R), which is known as the Hardy space of the upper half-plane. This is because a progressive function has the Fourier inversion formula :f(t) = \int_0^\infty e^ \hat f(s)\, ds and hence extends to a holomorphic function on the upper half-plane In mathematics, the upper half-plane, \,\mathcal\,, is the set of points in the Cartesian plane with > 0. Complex plane Mathematicians sometimes identify the Cartesian plane with the complex plane, and then the upper half-plane corresponds to t . ...
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