ConvolutionIntegral expressing the amount of overlap of one function as it is shifted over anotherVisual comparison of convolution, cross-correlation, and autocorrelation. For the operations involving function f{\displaystyle f}, and assuming the height of f{\displaystyle f} is 1.0, the value of the result at 5 different points is indicated by the shaded area below each point.
Inverse functionIn mathematics, the inverse function of a functionf (also called the inverse of f) is a function that undoes the operation of f. The inverse of f exists if and only iff is bijective, and if it exists, is denoted by f−1.{\displaystyle f^{-1}.}For a function f:X→Y{\displaystyle f\colon X\to Y}, its inverse f−1:Y→X{\displaystyle f^{-1}\colon Y\to X} admits an explicit description: it sends each element y∈Y{\displaystyle y\in Y} to the unique element x∈X{\displaystyle x\in X} such that f(x) = y. As an example, consider the real-valued function of a real variable given by f(x) = 5x − 7.
Signal processingSignal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing signals, such as sound, images, potential fields, seismic signals, altimetry processing, and scientific measurements. Signal processing techniques are used to optimize transmissions, digital storage efficiency, correcting distorted signals, improve subjective video quality, and to detect or pinpoint components of interest in a measured signal.
Norbert WienerNorbert Wiener (November 26, 1894 – March 18, 1964) was an American computer scientist, mathematician, and philosopher. He became a professor of mathematics at the Massachusetts Institute of Technology (MIT). A child prodigy, Wiener later became an early researcher in stochastic and mathematical noise processes, contributing work relevant to electronic engineering, electronic communication, and control systems.
Signal-to-noise ratioSignal-to-noise ratio (SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. SNR is defined as the ratio of signal power to noise power, often expressed in decibels. A ratio higher than 1:1 (greater than 0 dB) indicates more signal than noise.
MathematicsMathematics is a field of knowledge concerned with abstract concepts such as numbers, geometric shapes, sets, functions, and probabilities. It uses logical reasoning and proof to study and establish their properties, often expressed as theorems, formulas, and equations. Mathematics is used to model and solve problems in science, engineering, technology, economics, and everyday life.
Weather forecastingApplication of science and technologyForecast of surface pressures five days into the future for the North Pacific, North America, and the North Atlantic OceanWeather forecasting or weather prediction is the application of science and technology to predict the conditions of the atmosphere for a given location and time. People have attempted to predict the weather informally for thousands of years and formally since the 19th century.
World War IIGlobal conflict from 1939 to 1945BelligerentsAlliesAxisCommanders and leadersMain Allied leaders: Joseph StalinFranklin D. RooseveltWinston ChurchillChiang Kai-shekMain Axis leaders: Adolf HitlerHirohitoBenito MussoliniCasualties and losses 60–75 million deaths (military and civilian) World War II, or the Second World War (1 September 1939 – 2 September 1945), was a global conflict between two coalitions: the Allies and the Axis powers.
Massachusetts Institute of TechnologyPrivate research university in Cambridge, Massachusetts, United States The Massachusetts Institute of Technology (MIT) is a privateresearch university in Cambridge, Massachusetts, United States. Founded in 1861 to advance "useful knowledge", the university has played a significant role in the development of many areas of technology and science. William Barton Rogers founded MIT to accelerate American industrialization through scientific knowledge.
EconomicsSocial science studying goods and servicesEuro coinsEconomics () is a social science that studies the production, distribution, and consumption of goods and services. Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analyses what is viewed as the basic elements of economies, including individual agents and markets, their interactions, and the outcomes of those interactions.Digital image processingDigital image processing is the use of a digital computer to process digital images through an algorithm. As a subcategory or field of digital signal processing, digital image processing has many advantages over analog image processing. It allows a much wider range of algorithms to be applied to the input data and can avoid problems such as the build-up of noise and distortion during processing.
Time seriesIn mathematics, a time series is a sequence of data points indexed, listed, or graphed in chronological order. Most commonly, a time series consists of observations recorded at successive equally spaced points in time. Thus, it represents a form of discrete-time data. A time series may describe measurements collected over seconds, days, years, or even centuries.*As an Amazon Associate I earn from qualifying purchases.