Antialias
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Antialias
In digital signal processing, spatial anti-aliasing is a technique for minimizing the distortion artifacts ( aliasing) when representing a high-resolution image at a lower resolution. Anti-aliasing is used in digital photography, computer graphics, digital audio, and many other applications. Anti-aliasing means removing signal components that have a higher frequency than is able to be properly resolved by the recording (or sampling) device. This removal is done before (re)sampling at a lower resolution. When sampling is performed without removing this part of the signal, it causes undesirable artifacts such as black-and-white noise. In signal acquisition and audio, anti-aliasing is often done using an analog anti-aliasing filter to remove the out-of-band component of the input signal prior to sampling with an analog-to-digital converter. In digital photography, optical anti-aliasing filters made of birefringent materials smooth the signal in the spatial optical domain. Th ...
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ClearType
ClearType is Microsoft's implementation of subpixel rendering technology in rendering text in a font system. ClearType attempts to improve the appearance of text on certain types of computer display screens by sacrificing color fidelity for additional intensity variation. This trade-off is asserted to work well on LCD flat panel monitors. ClearType was first announced at the November 1998 COMDEX exhibition. The technology was first introduced in software in January 2000 as an always-on feature of Microsoft Reader, which was released to the public in August 2000. ClearType was significantly changed with the introduction of DirectWrite in Windows 7. Background Computer displays where the positions of individual pixels are permanently fixed such as most modern flat panel displays can show saw-tooth edges when displaying small, high-contrast graphic elements, such as text. ClearType uses spatial anti-aliasing at the subpixel level to reduce visible artifacts on such displays when t ...
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Subpixel Rendering
Subpixel rendering is a way to increase the apparent resolution of a computer's liquid crystal display (LCD) or organic light-emitting diode (OLED) display by rendering pixels to take into account the screen type's physical properties. It takes advantage of the fact that each pixel on a color LCD is actually composed of individual red, green, and blue or other color subpixels to anti-alias text with greater detail or to increase the resolution of all image types on layouts which are specifically designed to be compatible with subpixel rendering. Background A single pixel on a color subpixelated display is made of several color primaries, typically three colored elements—ordered (on various displays) either as blue, green, and red (), or as red, green, and blue ( ). Some displays have more than three primaries, often called MultiPrimary, such as the combination of red, green, blue, and yellow (), or red, green, blue and white (W), or even red, green, blue, yellow, and cyan ( ...
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Digital Audio
Digital audio is a representation of sound recorded in, or converted into, digital form. In digital audio, the sound wave of the audio signal is typically encoded as numerical samples in a continuous sequence. For example, in CD audio, samples are taken 44,100 times per second, each with 16-bit sample depth. Digital audio is also the name for the entire technology of sound recording and reproduction using audio signals that have been encoded in digital form. Following significant advances in digital audio technology during the 1970s and 1980s, it gradually replaced analog audio technology in many areas of audio engineering, record production and telecommunications in the 1990s and 2000s In a digital audio system, an analog electrical signal representing the sound is converted with an analog-to-digital converter (ADC) into a digital signal, typically using pulse-code modulation (PCM). This digital signal can then be recorded, edited, modified, and copied using computer ...
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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 ...
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Pixel
In digital imaging, a pixel (abbreviated px), pel, or picture element is the smallest addressable element in a raster image, or the smallest point in an all points addressable display device. In most digital display devices, pixels are the smallest element that can be manipulated through software. Each pixel is a sample of an original image; more samples typically provide more accurate representations of the original. The intensity of each pixel is variable. In color imaging systems, a color is typically represented by three or four component intensities such as red, green, and blue, or cyan, magenta, yellow, and black. In some contexts (such as descriptions of camera sensors), ''pixel'' refers to a single scalar element of a multi-component representation (called a ''photosite'' in the camera sensor context, although ''sensel'' is sometimes used), while in yet other contexts (like MRI) it may refer to a set of component intensities for a spatial position. Etymology The w ...
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Sine
In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that of the hypotenuse. For an angle \theta, the sine and cosine functions are denoted simply as \sin \theta and \cos \theta. More generally, the definitions of sine and cosine can be extended to any real value in terms of the lengths of certain line segments in a unit circle. More modern definitions express the sine and cosine as infinite series, or as the solutions of certain differential equations, allowing their extension to arbitrary positive and negative values and even to complex numbers. The sine and cosine functions are commonly used to model periodic phenomena such as sound and lig ...
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Integer
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign (−1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface or blackboard bold \mathbb. The set of natural numbers \mathbb is a subset of \mathbb, which in turn is a subset of the set of all rational numbers \mathbb, itself a subset of the real numbers \mathbb. Like the natural numbers, \mathbb is countably infinite. An integer may be regarded as a real number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , and  are not. The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more general algebraic integers ...
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Amplitude
The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of amplitude (see below), which are all functions of the magnitude of the differences between the variable's extreme values. In older texts, the phase of a periodic function is sometimes called the amplitude. Definitions Peak amplitude & semi-amplitude For symmetric periodic waves, like sine waves, square waves or triangle waves ''peak amplitude'' and ''semi amplitude'' are the same. Peak amplitude In audio system measurements, telecommunications and others where the measurand is a signal that swings above and below a reference value but is not sinusoidal, peak amplitude is often used. If the reference is zero, this is the maximum absolute value of the signal; if the reference is a mean value (DC component), the peak amplitude is the maximu ...
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Basis Function
In mathematics, a basis function is an element of a particular basis for a function space. Every function in the function space can be represented as a linear combination of basis functions, just as every vector in a vector space can be represented as a linear combination of basis vectors. In numerical analysis and approximation theory, basis functions are also called blending functions, because of their use in interpolation: In this application, a mixture of the basis functions provides an interpolating function (with the "blend" depending on the evaluation of the basis functions at the data points). Examples Monomial basis for ''Cω'' The monomial basis for the vector space of analytic functions is given by \. This basis is used in Taylor series, amongst others. Monomial basis for polynomials The monomial basis also forms a basis for the vector space of polynomials. After all, every polynomial can be written as a_0 + a_1x^1 + a_2x^2 + \cdots + a_n x^n for some n \in \mathb ...
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Fourier Transform
A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, which will output a function depending on temporal frequency or spatial frequency respectively. That process is also called ''analysis''. An example application would be decomposing the waveform of a musical chord into terms of the intensity of its constituent pitches. The term ''Fourier transform'' refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of space or time. The Fourier transform of a function is a complex-valued function representing the complex sinusoids that comprise the original function. For each frequency, the magnitude (absolute value) of the complex value represents the amplitude of a constituent complex sinusoid with that ...
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Bicubic Interpolation
In mathematics, bicubic interpolation is an extension of cubic interpolation (not to be confused with cubic spline interpolation, a method of applying cubic interpolation to a data set) for interpolating data points on a two-dimensional regular grid. The interpolated surface (meaning the kernel shape, not the image) is smoother than corresponding surfaces obtained by bilinear interpolation or nearest-neighbor interpolation. Bicubic interpolation can be accomplished using either Lagrange polynomials, cubic splines, or cubic convolution algorithm. In image processing, bicubic interpolation is often chosen over bilinear or nearest-neighbor interpolation in image resampling, when speed is not an issue. In contrast to bilinear interpolation, which only takes 4 pixels (2×2) into account, bicubic interpolation considers 16 pixels (4×4). Images resampled with bicubic interpolation can have different interpolation artifacts, depending on the b and c values chosen. Computation ...
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