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Aliasing
In signal processing and related disciplines, aliasing is an effect that causes different signals to become indistinguishable (or ''aliases'' of one another) when sampled. It also often refers to the distortion or artifact that results when a signal reconstructed from samples is different from the original continuous signal. Aliasing can occur in signals sampled in time, for instance digital audio, or the stroboscopic effect, and is referred to as temporal aliasing. It can also occur in spatially sampled signals (e.g. moiré patterns in digital images); this type of aliasing is called spatial aliasing. Aliasing is generally avoided by applying low-pass filters or anti-aliasing filters (AAF) to the input signal before sampling and when converting a signal from a higher to a lower sampling rate. Suitable reconstruction filtering should then be used when restoring the sampled signal to the continuous domain or converting a signal from a lower to a higher sampling rate. For spa ...
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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 ...
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Sampling (signal Processing)
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 ...
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Sampling Rate
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 Sample (statistics), 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 samp ...
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Multisample Anti-aliasing
Multisample anti-aliasing (MSAA) is a type of spatial anti-aliasing, a technique used in computer graphics to remove jaggies. Definition The term generally refers to a special case of supersampling. Initial implementations of full-scene anti-aliasing ( FSAA) worked conceptually by simply rendering a scene at a higher resolution, and then downsampling to a lower-resolution output. Most modern GPUs are capable of this form of anti-aliasing, but it greatly taxes resources such as texture, bandwidth, and fillrate. (If a program is highly TCL-bound or CPU-bound, supersampling can be used without much performance hit.) According to the OpenGL GL_ARB_multisample specification, "multisampling" refers to a specific optimization of supersampling. The specification dictates that the renderer evaluate the fragment program once per pixel, and only "truly" supersample the depth and stencil values. (This is not the same as supersampling but, by the OpenGL 1.5 specification, the definition ha ...
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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 ...
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Spatial Anti-aliasing
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. The anti-a ...
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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 ...
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Spatial Anti-aliasing
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. The anti-a ...
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Moiré Pattern
In mathematics, physics, and art, moiré patterns ( , , ) or moiré fringes are large-scale interference patterns that can be produced when an opaque ruled pattern with transparent gaps is overlaid on another similar pattern. For the moiré interference pattern to appear, the two patterns must not be completely identical, but rather displaced, rotated, or have slightly different pitch. Moiré patterns appear in many situations. In printing, the printed pattern of dots can interfere with the image. In television and digital photography, a pattern on an object being photographed can interfere with the shape of the light sensors to generate unwanted artifacts. They are also sometimes created deliberately – in micrometers they are used to amplify the effects of very small movements. In physics, its manifestation is wave interference such as that seen in the double-slit experiment and the beat phenomenon in acoustics. Etymology The term originates from '' moire'' (''moiré' ...
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Negative Frequency
The concept of signed frequency (negative and positive frequency) can indicate both the rate and sense of rotation; it can be as simple as a wheel rotating clockwise or counterclockwise. The rate is expressed in units such as revolutions (a.k.a. ''cycles'') per second (hertz) or radian/second (where 1 cycle corresponds to 2''π'' radians). Sinusoids Let be a nonnegative angular frequency with units of radians/second. Then the function has slope , which is called a negative frequency. But when the function is used as the argument of a cosine operator, the result is indistinguishable from . Similarly, is indistinguishable from . Thus any sinusoid can be represented in terms of positive frequencies. The sign of the underlying phase slope is ambiguous. The ambiguity is resolved when the cosine and sine operators can be observed simultaneously, because leads by 1/4 cycle (= ''π''/2 radians) when , and lags by 1/4 cycle when . Similarly, a vector, , rotates counter ...
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Wagon Wheel Effect
The wagon-wheel effect (alternatively called stagecoach-wheel effect or stroboscopic effect) is an optical illusion in which a spoked wheel appears to rotate differently from its true rotation. The wheel can appear to rotate more slowly than the true rotation, it can appear stationary, or it can appear to rotate in the opposite direction from the true rotation. This last form of the effect is sometimes called the reverse rotation effect. The wagon-wheel effect is most often seen in film or television depictions of stagecoaches or wagons in Western movies, although recordings of any regularly spoked rotating object will show it, such as helicopter rotors, aircraft propellers and car rims. In these recorded media, the effect is a result of temporal aliasing. It can also commonly be seen when a rotating wheel is illuminated by flickering light. These forms of the effect are known as stroboscopic effects: the original smooth rotation of the wheel is visible only intermittently. A ver ...
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Fast Approximate Anti-aliasing
Fast approximate anti-aliasing (FXAA) is a screen-space anti-aliasing algorithm created by Timothy Lottes at Nvidia. FXAA 3 is released under a public domain license. A later version, FXAA 3.11, is released under a 3-clause BSD license. Algorithm description # The input data is the rendered image and optionally the luminance data. # Acquire the luminance data. This data could be passed into the FXAA algorithm from the rendering step as an alpha channel embedded into the image to be antialiased, calculated from the rendered image, or approximated by using the green channel as the luminance data. # Find high contrast pixels by using a high pass filter that uses the luminance data. Low contrast pixels that are found are excluded from being further altered by FXAA. The high pass filter that excludes low contrast pixels can be tuned to balance speed and sensitivity. # Use contrast between adjacent pixels to heuristically find edges, and determine whether the edges are in the horizo ...
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