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Nonlinear Filter
In signal processing, a nonlinear (or non-linear) filter is a filter whose output is not a linear function of its input. That is, if the filter outputs signals ''R'' and ''S'' for two input signals ''r'' and ''s'' separately, but does not always output ''αR'' + ''βS'' when the input is a linear combination ''αr'' + ''βs''. Both continuous-domain and discrete-domain filters may be nonlinear. A simple example of the former would be an electrical device whose output voltage ''R''(''t'') at any moment is the square of the input voltage ''r''(''t''); or which is the input clipped to a fixed range 'a'',''b'' namely ''R''(''t'') = max(''a'', min(''b'', ''r''(''t''))). An important example of the latter is the running-median filter, such that every output sample ''R''''i'' is the median of the last three input samples ''r''''i'', ''r''''i''−1, ''r''''i''−2. Like linear filters, nonlinear filters may be shift invariant or not. Non-linear filters hav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Signal Processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as sound, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, digital storage efficiency, correcting distorted signals, subjective video quality and to also detect or pinpoint components of interest in a measured signal. History According to Alan V. Oppenheim and Ronald W. Schafer, the principles of signal processing can be found in the classical numerical analysis techniques of the 17th century. They further state that the digital refinement of these techniques can be found in the digital control systems of the 1940s and 1950s. In 1948, Claude Shannon wrote the influential paper "A Mathematical Theory of Communication" which was published in the Bell System Technical Journal. The paper laid the groundwork for later development of information communication systems and the processing of signals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analog-to-digital Converter
In electronics, an analog-to-digital converter (ADC, A/D, or A-to-D) is a system that converts an analog signal, such as a sound picked up by a microphone or light entering a digital camera, into a digital signal. An ADC may also provide an isolated measurement such as an electronic device that converts an analog input voltage or current to a digital number representing the magnitude of the voltage or current. Typically the digital output is a two's complement binary number that is proportional to the input, but there are other possibilities. There are several ADC architectures. Due to the complexity and the need for precisely matched components, all but the most specialized ADCs are implemented as integrated circuits (ICs). These typically take the form of metal–oxide–semiconductor (MOS) mixed-signal integrated circuit chips that integrate both analog and digital circuits. A digital-to-analog converter (DAC) performs the reverse function; it converts a digital s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiplicative Noise
In signal processing, the term multiplicative noise refers to an unwanted random signal that gets multiplied into some relevant signal during capture, transmission, or other processing. An important example is the speckle noise commonly observed in radar imagery. Examples of multiplicative noise affecting digital photographs are proper shadows due to undulations on the surface of the imaged objects, shadows cast by complex objects like foliage and Venetian blinds, dark spots caused by dust in the lens or image sensor, and variations in the gain of individual elements of the image sensor An image sensor or imager is a sensor that detects and conveys information used to make an image. It does so by converting the variable attenuation of light waves (as they pass through or reflect off objects) into signals, small bursts of c ... array. Maria Petrou, Costas Petrou (2010Image Processing: The Fundamentals John Wiley & Sons. 818 pages. References {{reflist Signal proce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bandpass Filter
A band-pass filter or bandpass filter (BPF) is a device that passes frequencies within a certain range and rejects ( attenuates) frequencies outside that range. Description In electronics and signal processing, a filter is usually a two-port circuit or device which removes frequency components of a signal (an alternating voltage or current). A band-pass filter allows through components in a specified band of frequencies, called its '' passband'' but blocks components with frequencies above or below this band. This contrasts with a high-pass filter, which allows through components with frequencies above a specific frequency, and a low-pass filter, which allows through components with frequencies below a specific frequency. In digital signal processing, in which signals represented by digital numbers are processed by computer programs, a band-pass filter is a computer algorithm that performs the same function. The term band-pass filter is also used for optical fil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frequency Domain
In physics, electronics, control systems engineering, and statistics, the frequency domain refers to the analysis of mathematical functions or signals with respect to frequency, rather than time. Put simply, a time-domain graph shows how a signal changes over time, whereas a frequency-domain graph shows how much of the signal lies within each given frequency band over a range of frequencies. A frequency-domain representation can also include information on the phase shift that must be applied to each sinusoid in order to be able to recombine the frequency components to recover the original time 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 transform, which converts a time function into a complex valued sum or integral of sine waves of different frequencies, with amplitudes and phases, each of which represents a frequency component. The "spectr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shannon's Theorem
In information theory, the noisy-channel coding theorem (sometimes Shannon's theorem or Shannon's limit), establishes that for any given degree of noise contamination of a communication channel, it is possible to communicate discrete data (digital information) nearly error-free up to a computable maximum rate through the channel. This result was presented by Claude Shannon in 1948 and was based in part on earlier work and ideas of Harry Nyquist and Ralph Hartley. The Shannon limit or Shannon capacity of a communication channel refers to the maximum rate of error-free data that can theoretically be transferred over the channel if the link is subject to random data transmission errors, for a particular noise level. It was first described by Shannon (1948), and shortly after published in a book by Shannon and Warren Weaver entitled ''The Mathematical Theory of Communication'' (1949). This founded the modern discipline of information theory. Overview Stated by Claude Shannon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kalman Filter
For statistics and control theory, Kalman filtering, also known as linear quadratic estimation (LQE), is an algorithm that uses a series of measurements observed over time, including statistical noise and other inaccuracies, and produces estimates of unknown variables that tend to be more accurate than those based on a single measurement alone, by estimating a joint probability distribution over the variables for each timeframe. The filter is named after Rudolf E. Kálmán, who was one of the primary developers of its theory. This digital filter is sometimes termed the ''Stratonovich–Kalman–Bucy filter'' because it is a special case of a more general, nonlinear filter developed somewhat earlier by the Soviet mathematician Ruslan Stratonovich. In fact, some of the special case linear filter's equations appeared in papers by Stratonovich that were published before summer 1960, when Kalman met with Stratonovich during a conference in Moscow. Kalman filtering has numerous te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gaussian Noise
Gaussian noise, named after Carl Friedrich Gauss, is a term from signal processing theory denoting a kind of signal noise that has a probability density function (pdf) equal to that of the normal distribution (which is also known as the Gaussian distribution). In other words, the values that the noise can take are Gaussian-distributed. The probability density function p of a Gaussian random variable z is given by: : p_G(z) = \frac e^ where z represents the grey level, \mu the mean grey value and \sigma its standard deviation. A special case is ''White Gaussian noise'', in which the values at any pair of times are identically distributed and statistically independent (and hence uncorrelated). In communication channel testing and modelling, Gaussian noise is used as additive white noise to generate additive white Gaussian noise. In telecommunications and computer networking, communication channels can be affected by wideband Gaussian noise coming from many natural sources, such ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Scalar (mathematics)
A scalar is an element of a field which is used to define a ''vector space''. In linear algebra, real numbers or generally elements of a field are called scalars and relate to vectors in an associated vector space through the operation of scalar multiplication (defined in the vector space), in which a vector can be multiplied by a scalar in the defined way to produce another vector. Generally speaking, a vector space may be defined by using any field instead of real numbers (such as complex numbers). Then scalars of that vector space will be elements of the associated field (such as complex numbers). A scalar product operation – not to be confused with scalar multiplication – may be defined on a vector space, allowing two vectors to be multiplied in the defined way to produce a scalar. A vector space equipped with a scalar product is called an inner product space. A quantity described by multiple scalars, such as having both direction and magnitude, is called a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linearity
Linearity is the property of a mathematical relationship ('' function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear relationship of voltage and current in an electrical conductor (Ohm's law), and the relationship of mass and weight. By contrast, more complicated relationships are ''nonlinear''. Generalized for functions in more than one dimension, linearity means the property of a function of being compatible with addition and scaling, also known as the superposition principle. The word linear comes from Latin ''linearis'', "pertaining to or resembling a line". In mathematics In mathematics, a linear map or linear function ''f''(''x'') is a function that satisfies the two properties: * Additivity: . * Homogeneity of degree 1: for all α. These properties are known as the superposition principle. In this definition, ''x'' is not necessarily a r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear System
In systems theory, a linear system is a mathematical model of a system based on the use of a linear operator. Linear systems typically exhibit features and properties that are much simpler than the nonlinear case. As a mathematical abstraction or idealization, linear systems find important applications in automatic control theory, signal processing, and telecommunications. For example, the propagation medium for wireless communication systems can often be modeled by linear systems. Definition A general deterministic system can be described by an operator, that maps an input, as a function of to an output, a type of black box description. A system is linear if and only if it satisfies the superposition principle, or equivalently both the additivity and homogeneity properties, without restrictions (that is, for all inputs, all scaling constants and all time.) The superposition principle means that a linear combination of inputs to the system produces a linear combinat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frequency Response
In signal processing and electronics, the frequency response of a system is the quantitative measure of the magnitude and phase of the output as a function of input frequency. The frequency response is widely used in the design and analysis of systems, such as audio and control systems, where they simplify mathematical analysis by converting governing differential equations into algebraic equations. In an audio system, it may be used to minimize audible distortion by designing components (such as microphones, amplifiers and loudspeakers) so that the overall response is as flat (uniform) as possible across the system's bandwidth. In control systems, such as a vehicle's cruise control, it may be used to assess system stability, often through the use of Bode plots. Systems with a specific frequency response can be designed using analog and digital filters. The frequency response characterizes systems in the frequency domain, just as the impulse response characterizes systems ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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