|
Time Domain
In mathematics and signal processing, the time domain is a representation of how a signal, function, or data set varies with time. It is used for the analysis of mathematical functions, physical signals or time series of economic or environmental data. In the time domain, the independent variable is time, and the dependent variable is the value of the signal. This contrasts with the frequency domain, where the signal is represented by its constituent frequencies. For continuous-time signals, the value of the signal is defined for all real numbers representing time. For discrete-time signals, the value is known at discrete, often equally-spaced, time intervals. It is commonly visualized using a graph where the x-axis represents time and the y-axis represents the signal's value. An oscilloscope is a common tool used to visualize real-world signals in the time domain. Though most precisely referring to time in physics, the term ''time domain'' may occasionally informally ref ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time In Physics
In physics, time is defined by its operational definition, measurement: time is what a clock reads. In classical, non-relativistic physics, it is a scalar (physics), scalar quantity (often denoted by the symbol t) and, like length, mass, and electric charge, charge, is usually described as a fundamental quantity. Time can be combined mathematically with other physical quantities to Formal proof, derive other concepts such as motion (physics), motion, kinetic energy and time-dependent Field (physics), fields. '':category:Timekeeping, Timekeeping'' is a complex of technological and scientific issues, and part of the foundation of ''recordkeeping''. Markers of time Before there were clocks, time was measured by those physical processes which were understandable to each epoch of civilization: * the first appearance (see: heliacal rising) of Sirius to mark the flooding of the Nile each yearOtto Neugebauer ''The Exact Sciences in Antiquity''. Princeton: Princeton University Pre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Laplace Transform
In mathematics, the Laplace transform, named after Pierre-Simon Laplace (), is an integral transform that converts a Function (mathematics), function of a Real number, real Variable (mathematics), variable (usually t, in the ''time domain'') to a function of a Complex number, complex variable s (in the complex-valued frequency domain, also known as ''s''-domain, or ''s''-plane). The transform is useful for converting derivative, differentiation and integral, integration in the time domain into much easier multiplication and Division (mathematics), division in the Laplace domain (analogous to how logarithms are useful for simplifying multiplication and division into addition and subtraction). This gives the transform many applications in science and engineering, mostly as a tool for solving linear differential equations and dynamical systems by simplifying ordinary differential equations and integral equations into algebraic equation, algebraic polynomial equations, and by simplifyin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Transform
In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input then outputs another function that describes the extent to which various frequencies are present in the original function. The output of the transform is a complex-valued function of frequency. The term ''Fourier transform'' refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made, the output of the operation is sometimes called the frequency domain representation of the original function. The Fourier transform is analogous to decomposing the sound of a musical chord into the intensities of its constituent pitches. Functions that are localized in the time domain have Fourier transforms that are spread out across the frequency domain and vice versa, a phenomenon known as the uncertainty principle. The critical case for this principle is the Gaussian function, of substantial importance in probability theory and statist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frequency Domain
In mathematics, physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency (and possibly phase), rather than time, as in time series. While a time-domain graph shows how a signal changes over time, a frequency-domain graph shows how the signal is distributed within different frequency bands over a range of frequencies. A complex valued frequency-domain representation consists of both the magnitude and the phase of a set of sinusoids (or other basis waveforms) at the frequency components of the signal. Although it is common to refer to the magnitude portion (the real valued frequency-domain) as the frequency response of a signal, the phase portion is required to uniquely define the signal. A given function or signal can be converted between the time and frequency domains with a pair of mathematical operators called transforms. An example is the Fourier transfo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hertz
The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), often described as being equivalent to one event (or Cycle per second, cycle) per second. The hertz is an SI derived unit whose formal expression in terms of SI base units is 1/s or s−1, meaning that one hertz is one per second or the Inverse second, reciprocal of one second. It is used only in the case of periodic events. It is named after Heinrich Hertz, Heinrich Rudolf Hertz (1857–1894), the first person to provide conclusive proof of the existence of electromagnetic waves. For high frequencies, the unit is commonly expressed in metric prefix, multiples: kilohertz (kHz), megahertz (MHz), gigahertz (GHz), terahertz (THz). Some of the unit's most common uses are in the description of periodic waveforms and musical tones, particularly those used in radio- and audio-related applications. It is also used to describe the clock speeds at which computers and other electronics are driven. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unit Of Measurement
A unit of measurement, or unit of measure, is a definite magnitude (mathematics), magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other quantity of that kind can be expressed as a multiple of the unit of measurement. For example, a length is a physical quantity. The metre (symbol m) is a unit of length that represents a definite predetermined length. For instance, when referencing "10 metres" (or 10 m), what is actually meant is 10 times the definite predetermined length called "metre". The definition, agreement, and practical use of units of measurement have played a crucial role in human endeavour from early ages up to the present. A multitude of System of measurement, systems of units used to be very common. Now there is a global standard, the International System of Units (SI), the modern form of the metric system. In trade, weights and measures are often a su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Second
The second (symbol: s) is a unit of time derived from the division of the day first into 24 hours, then to 60 minutes, and finally to 60 seconds each (24 × 60 × 60 = 86400). The current and formal definition in the International System of Units (SI) is more precise: The second ..is defined by taking the fixed numerical value of the caesium frequency, Δ''ν''Cs, the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, to be when expressed in the unit Hz, which is equal to s−1. This current definition was adopted in 1967 when it became feasible to define the second based on fundamental properties of nature with caesium clocks. As the speed of Earth's rotation varies and is slowing ever so slightly, a leap second is added at irregular intervals to civil time to keep clocks in sync with Earth's rotation. The definition that is based on of a rotation of the earth is still used by the Universal Time 1 (UT1) system. Etymology "Minute" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Communication Engineering
Telecommunications engineering is a subfield of electronics engineering which seeks to design and devise systems of communication at a distance. The work ranges from basic circuit design to strategic mass developments. A telecommunication engineer is responsible for designing and overseeing the installation of telecommunications equipment and facilities, such as complex electronic switching system, and other plain old telephone service facilities, optical fiber cabling, IP networks, and microwave transmission systems. Telecommunications engineering also overlaps with broadcast engineering. Telecommunication is a diverse field of engineering connected to electronic, civil and systems engineering. Ultimately, telecom engineers are responsible for providing high-speed data transmission services. They use a variety of equipment and transport media to design the telecom network infrastructure; the most common media used by wired telecommunications today are twisted pair, coax ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fourier Transform Time And Frequency Domains (small)
Fourier may refer to: * Fourier (surname), French surname Mathematics *Fourier series, a weighted sum of sinusoids having a common period, the result of Fourier analysis of a periodic function *Fourier analysis, the description of functions as sums of sinusoids *Fourier transform, the type of linear canonical transform that is the generalization of the Fourier series *Fourier operator, the kernel of the Fredholm integral of the first kind that defines the continuous Fourier transform * Fourier inversion theorem, any one of several theorems by which Fourier inversion recovers a function from its Fourier transform * Short-time Fourier transform or short-term Fourier transform (STFT), a Fourier transform during a short term of time, used in the area of signal analysis *Fractional Fourier transform (FRFT), a linear transformation generalizing the Fourier transform, used in the area of harmonic analysis * Discrete-time Fourier transform (DTFT), the reverse of the Fourier series, a speci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spatial Frequency
In mathematics, physics, and engineering, spatial frequency is a characteristic of any structure that is periodic across position in space. The spatial frequency is a measure of how often sinusoidal components (as determined by the Fourier transform) of the structure repeat per unit of distance. The SI unit of spatial frequency is the reciprocal metre (m−1), (11 pages) although cycle (rotational unit), cycles per (c/m) is also common. In image-processing applications, spatial freque ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Space
Space is a three-dimensional continuum containing positions and directions. In classical physics, physical space is often conceived in three linear dimensions. Modern physicists usually consider it, with time, to be part of a boundless four-dimensional continuum known as '' spacetime''. The concept of space is considered to be of fundamental importance to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, a relationship between entities, or part of a conceptual framework. In the 19th and 20th centuries mathematicians began to examine geometries that are non-Euclidean, in which space is conceived as '' curved'', rather than '' flat'', as in the Euclidean space. According to Albert Einstein's theory of general relativity, space around gravitational fields deviates from Euclidean space. Experimental tests of general relativity have confirmed that non-Euclidean geometries provide a bet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
