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Zero-order Hold
The zero-order hold (ZOH) is a mathematical model of the practical signal reconstruction done by a conventional digital-to-analog converter (DAC). That is, it describes the effect of converting a discrete-time signal to a continuous-time signal by holding each sample value for one sample interval. It has several applications in electrical communication. Time-domain model A zero-order hold reconstructs the following continuous-time waveform from a sample sequence ''x'' 'n'' assuming one sample per time interval ''T'': x_(t)\,= \sum_^ x cdot \mathrm \left(\frac \right) where \mathrm(\cdot) is the rectangular function. The function \mathrm \left(\frac \right) is depicted in Figure 1, and x_(t) is the piecewise-constant signal depicted in Figure 2. Frequency-domain model The equation above for the output of the ZOH can also be modeled as the output of a linear time-invariant filter with impulse response equal to a rect function, and with input being a sequence of dirac im ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Signal Reconstruction
In signal processing, reconstruction usually means the determination of an original continuous signal from a sequence of equally spaced samples. This article takes a generalized abstract mathematical approach to signal sampling and reconstruction. For a more practical approach based on band-limited signals, see Whittaker–Shannon interpolation formula. General principle Let ''F'' be any sampling method, i.e. a linear map from the Hilbert space of square-integrable functions L^2 to complex space \mathbb C^n. In our example, the vector space of sampled signals \mathbb C^n is ''n''-dimensional complex space. Any proposed inverse ''R'' of ''F'' (''reconstruction formula'', in the lingo) would have to map \mathbb C^n to some subset of L^2. We could choose this subset arbitrarily, but if we're going to want a reconstruction formula ''R'' that is also a linear map, then we have to choose an ''n''-dimensional linear subspace of L^2. This fact that the dimensions have to agree is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Filter (signal Processing)
In signal processing, a filter is a device or process that removes some unwanted components or features from a signal. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal. Most often, this means removing some frequencies or frequency bands. However, filters do not exclusively act in the frequency domain; especially in the field of image processing many other targets for filtering exist. Correlations can be removed for certain frequency components and not for others without having to act in the frequency domain. Filters are widely used in electronics and telecommunication, in radio, television, audio recording, radar, control systems, music synthesis, image processing, and computer graphics. There are many different bases of classifying filters and these overlap in many different ways; there is no simple hierarchical classification. Filters may be: *non-linear or linear *time-variant or t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Signal Processing
Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations. The digital signals processed in this manner are a sequence of numbers that represent samples of a continuous variable in a domain such as time, space, or frequency. In digital electronics, a digital signal is represented as a pulse train, which is typically generated by the switching of a transistor. Digital signal processing and analog signal processing are subfields of signal processing. DSP applications include audio and speech processing, sonar, radar and other sensor array processing, spectral density estimation, statistical signal processing, digital image processing, data compression, video coding, audio coding, image compression, signal processing for telecommunications, control systems, biomedical engineering, and seismology, among others. DSP can involve linear or nonli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discretization
In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers. Dichotomization is the special case of discretization in which the number of discrete classes is 2, which can approximate a continuous variable as a binary variable (creating a dichotomy for modeling purposes, as in binary classification). Discretization is also related to discrete mathematics, and is an important component of granular computing. In this context, ''discretization'' may also refer to modification of variable or category ''granularity'', as when multiple discrete variables are aggregated or multiple discrete categories fused. Whenever continuous data is discretized, there is always some amount of discretization error. The goal is to reduce the amount to a level conside ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First-order Hold
First-order hold (FOH) is a mathematical model of the practical reconstruction of sampled signals that could be done by a conventional digital-to-analog converter (DAC) and an analog circuit called an integrator. For FOH, the signal is reconstructed as a piecewise linear approximation to the original signal that was sampled. A mathematical model such as FOH (or, more commonly, the zero-order hold) is necessary because, in the sampling and reconstruction theorem, a sequence of Dirac impulses, ''x''s(''t''), representing the discrete samples, ''x''(''nT''), is low-pass filtered to recover the original signal that was sampled, ''x''(''t''). However, outputting a sequence of Dirac impulses is impractical. Devices can be implemented, using a conventional DAC and some linear analog circuitry, to reconstruct the piecewise linear output for either predictive or delayed FOH. Even though this is ''not'' what is physically done, an identical output can be generated by applying the hypothe ... [...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 signa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sample And Hold
In electronics, a sample and hold (also known as sample and follow) circuit is an analog device that samples (captures, takes) the voltage of a continuously varying analog signal and holds (locks, freezes) its value at a constant level for a specified minimum period of time. Sample and hold circuits and related peak detectors are the elementary analog memory devices. They are typically used in analog-to-digital converters to eliminate variations in input signal that can corrupt the conversion process.Kefauver and Patschke, p. 37. They are also used in electronic music, for instance to impart a random quality to successively-played notes. A typical sample and hold circuit stores electric charge in a capacitor and contains at least one switching device such as a FET (field effect transistor) switch and normally one operational amplifier.Horowitz and Hill, p. 220. To sample the input signal, the switch connects the capacitor to the output of a buffer amplifier. The buffer ampli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nyquist Frequency
In signal processing, the Nyquist frequency (or folding frequency), named after Harry Nyquist, is a characteristic of a sampler, which converts a continuous function or signal into a discrete sequence. In units of cycles per second ( Hz), its value is one-half of the sampling rate (samples per second). When the highest frequency (bandwidth) of a signal is less than the Nyquist frequency of the sampler, the resulting discrete-time sequence is said to be free of the distortion known as aliasing, and the corresponding sample rate is said to be above the Nyquist rate for that particular signal. In a typical application of sampling, one first chooses the highest frequency to be preserved and recreated, based on the expected content (voice, music, etc.) and desired fidelity. Then one inserts an anti-aliasing filter ahead of the sampler. Its job is to attenuate the frequencies above that limit. Finally, based on the characteristics of the filter, one chooses a sample rate (and corre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roll-off
Roll-off is the steepness of a Transfer function, transfer function with frequency, particularly in network analysis (electrical circuits), electrical network analysis, and most especially in connection with filter (signal processing), filter circuits in the transition between a passband and a stopband. It is most typically applied to the insertion loss of the network, but can, in principle, be applied to any relevant function of frequency, and any technology, not just electronics. It is usual to measure roll-off as a function of logarithmic scale, logarithmic frequency; consequently, the units of roll-off are either decibels per decade (log scale), decade (dB/decade), where a decade is a tenfold increase in frequency, or decibels per octave (electronics), octave (dB/8ve), where an octave is a twofold increase in frequency. The concept of roll-off stems from the fact that in many networks roll-off tends towards a constant gradient at frequencies well away from the cut-off freque ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Piecewise Constant
In mathematics, a function on the real numbers is called a step function if it can be written as a finite linear combination of indicator functions of intervals. Informally speaking, a step function is a piecewise constant function having only finitely many pieces. Definition and first consequences A function f\colon \mathbb \rightarrow \mathbb is called a step function if it can be written as :f(x) = \sum\limits_^n \alpha_i \chi_(x), for all real numbers x where n\ge 0, \alpha_i are real numbers, A_i are intervals, and \chi_A is the indicator function of A: :\chi_A(x) = \begin 1 & \text x \in A \\ 0 & \text x \notin A \\ \end In this definition, the intervals A_i can be assumed to have the following two properties: # The intervals are pairwise disjoint: A_i \cap A_j = \emptyset for i \neq j # The union of the intervals is the entire real line: \bigcup_^n A_i = \mathbb R. Indeed, if that is not the case to start with, a different set of intervals can be picked for whi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dirac Delta
In mathematics, the Dirac delta distribution ( distribution), also known as the unit impulse, is a generalized function or distribution over the real numbers, whose value is zero everywhere except at zero, and whose integral over the entire real line is equal to one. The current understanding of the unit impulse is as a linear functional that maps every continuous function (e.g., f(x)) to its value at zero of its domain (f(0)), or as the weak limit of a sequence of bump functions (e.g., \delta(x) = \lim_ \frace^), which are zero over most of the real line, with a tall spike at the origin. Bump functions are thus sometimes called "approximate" or "nascent" delta distributions. The delta function was introduced by physicist Paul Dirac as a tool for the normalization of state vectors. It also has uses in probability theory and signal processing. Its validity was disputed until Laurent Schwartz developed the theory of distributions where it is defined as a linear form acting on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transfer Function
In engineering, a transfer function (also known as system function or network function) of a system, sub-system, or component is a function (mathematics), mathematical function that mathematical model, theoretically models the system's output for each possible input. They are widely used in electronics and control systems. In some simple cases, this function is a two-dimensional graph (function), graph of an independent scalar (mathematics), scalar input versus the dependent scalar output, called a transfer curve or characteristic curve. Transfer functions for components are used to design and analyze systems assembled from components, particularly using the block diagram technique, in electronics and control theory. The dimensions and units of the transfer function model the output response of the device for a range of possible inputs. For example, the transfer function of a two-port electronic circuit like an amplifier might be a two-dimensional graph of the scalar voltage at th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
