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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] |
Digital-to-analog Converter
In electronics, a digital-to-analog converter (DAC, D/A, D2A, or D-to-A) is a system that converts a digital signal into an analog signal. An analog-to-digital converter (ADC) performs the reverse function. There are several DAC architectures; the suitability of a DAC for a particular application is determined by figures of merit including: resolution, maximum sampling frequency and others. Digital-to-analog conversion can degrade a signal, so a DAC should be specified that has insignificant errors in terms of the application. DACs are commonly used in music players to convert digital data streams into analog audio signals. They are also used in televisions and mobile phones to convert digital video data into analog video signals. These two applications use DACs at opposite ends of the frequency/resolution trade-off. The audio DAC is a low-frequency, high-resolution type while the video DAC is a high-frequency low- to medium-resolution type. Due to the comple ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sinc Function
In mathematics, physics and engineering, the sinc function, denoted by , has two forms, normalized and unnormalized.. In mathematics, the historical unnormalized sinc function is defined for by \operatornamex = \frac. Alternatively, the unnormalized sinc function is often called the sampling function, indicated as Sa(''x''). In digital signal processing and information theory, the normalized sinc function is commonly defined for by \operatornamex = \frac. In either case, the value at is defined to be the limiting value \operatorname0 := \lim_\frac = 1 for all real . The normalization causes the definite integral of the function over the real numbers to equal 1 (whereas the same integral of the unnormalized sinc function has a value of ). As a further useful property, the zeros of the normalized sinc function are the nonzero integer values of . The normalized sinc function is the Fourier transform of the rectangular function with no scaling. It is used in the conc ... [...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 l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bilinear Interpolation
In mathematics, bilinear interpolation is a method for interpolating functions of two variables (e.g., ''x'' and ''y'') using repeated linear interpolation. It is usually applied to functions sampled on a 2D rectilinear grid, though it can be generalized to functions defined on the vertices of (a mesh of) arbitrary convex quadrilaterals. Bilinear interpolation is performed using linear interpolation first in one direction, and then again in the other direction. Although each step is linear in the sampled values and in the position, the interpolation as a whole is not linear but rather quadratic in the sample location. Bilinear interpolation is one of the basic resampling techniques in computer vision and image processing, where it is also called bilinear filtering or bilinear texture mapping. Computation Suppose that we want to find the value of the unknown function ''f'' at the point (''x'', ''y''). It is assumed that we know the value of ''f'' at the four points ''Q''11 = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rectangular Function
The rectangular function (also known as the rectangle function, rect function, Pi function, Heaviside Pi function, gate function, unit pulse, or the normalized boxcar function) is defined as \operatorname(t) = \Pi(t) = \left\{\begin{array}{rl} 0, & \text{if } , t, > \frac{1}{2} \\ \frac{1}{2}, & \text{if } , t, = \frac{1}{2} \\ 1, & \text{if } , t, \frac{1}{2} \\ \frac{1}{2} & \mbox{if } , t, = \frac{1}{2} \\ 1 & \mbox{if } , t, < \frac{1}{2}. \\ \end{cases} See also * * *Step function
In mathematics, a function on t ...
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Extrapolate
In mathematics, extrapolation is a type of estimation, beyond the original observation range, of the value of a variable on the basis of its relationship with another variable. It is similar to interpolation, which produces estimates between known observations, but extrapolation is subject to greater uncertainty and a higher risk of producing meaningless results. Extrapolation may also mean extension of a method, assuming similar methods will be applicable. Extrapolation may also apply to human experience to project, extend, or expand known experience into an area not known or previously experienced so as to arrive at a (usually conjectural) knowledge of the unknownExtrapolation entry at Merriam–Webster (e.g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Filter
In signal processing, a digital filter is a system that performs mathematical operations on a sampled, discrete-time signal to reduce or enhance certain aspects of that signal. This is in contrast to the other major type of electronic filter, the analog filter, which is typically an electronic circuit operating on continuous-time analog signals. A digital filter system usually consists of an analog-to-digital converter (ADC) to sample the input signal, followed by a microprocessor and some peripheral components such as memory to store data and filter coefficients etc. Program Instructions (software) running on the microprocessor implement the digital filter by performing the necessary mathematical operations on the numbers received from the ADC. In some high performance applications, an FPGA or ASIC is used instead of a general purpose microprocessor, or a specialized digital signal processor (DSP) with specific paralleled architecture for expediting operations such as fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Causal System
In control theory, a causal system (also known as a physical or nonanticipative system) is a system where the output depends on past and current inputs but not future inputs—i.e., the output y(t_) depends only on the input x(t) for values of t \le t_. The idea that the output of a function at any time depends only on past and present values of input is defined by the property commonly referred to as causality. A system that has ''some'' dependence on input values from the future (in addition to possible dependence on past or current input values) is termed a non-causal or acausal system, and a system that depends ''solely'' on future input values is an anticausal system. Note that some authors have defined an anticausal system as one that depends solely on future ''and present'' input values or, more simply, as a system that does not depend on past input values. Classically, nature or physical reality has been considered to be a causal system. Physics involving special rela ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sampling Frequency
In signal processing, sampling is the reduction of a continuous-time signal to a discrete-time signal. A common example is the conversion of a sound wave to a sequence of "samples". A sample is a value of the signal at a point in time and/or space; this definition differs from the usage in statistics, which refers to a set of such values. A sampler is a subsystem or operation that extracts samples from a continuous signal. A theoretical ideal sampler produces samples equivalent to the instantaneous value of the continuous signal at the desired points. The original signal can be reconstructed from a sequence of samples, up to the Nyquist limit, by passing the sequence of samples through a type of low-pass filter called a reconstruction filter. Theory Functions of space, time, or any other dimension can be sampled, and similarly in two or more dimensions. For functions that vary with time, let ''S''(''t'') be a continuous function (or "signal") to be sampled, and let samp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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