Digital signal processing
Digital signal processing 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 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. Digital signal processing and analog signal processing are subfields of signal processing. DSP applications include audio and speech processing, sonar and other sensor array processing, spectral density estimation, statistical signal processing, digital image processing, signal processing for telecommunications, control systems, biomedical engineering, among others. DSP can involve linear or nonlinear operations. Nonlinear signal processing is related to nonlinear system identification and can be implemented in the time and spatio-temporal domains; the application of digital computation to signal processing allows for many advantages over analog processing in many applications, such as error detection and correction in transmission as well as data compression.
DSP is applicable to static data. To digitally analyze and manipulate an analog signal, it must be digitized with an analog-to-digital converter. Sampling is carried out in two stages and quantization. Discretization means that the signal is divided into equal intervals of time, each interval is represented by a single measurement of amplitude. Quantization means. Rounding real numbers to integers is an example; the Nyquist–Shannon sampling theorem states that a signal can be reconstructed from its samples if the sampling frequency is greater than twice the highest frequency component in the signal. In practice, the sampling frequency is significantly higher than twice the Nyquist frequency. Theoretical DSP analyses and derivations are performed on discrete-time signal models with no amplitude inaccuracies, "created" by the abstract process of sampling. Numerical methods require a quantized signal, such as those produced by an ADC; the processed result might be a set of statistics. But it is another quantized signal, converted back to analog form by a digital-to-analog converter.
In DSP, engineers study digital signals in one of the following domains: time domain, spatial domain, frequency domain, wavelet domains. They choose the domain in which to process a signal by making an informed assumption as to which domain best represents the essential characteristics of the signal and the processing to be applied to it. A sequence of samples from a measuring device produces a temporal or spatial domain representation, whereas a discrete Fourier transform produces the frequency domain representation; the most common processing approach in the time or space domain is enhancement of the input signal through a method called filtering. Digital filtering consists of some linear transformation of a number of surrounding samples around the current sample of the input or output signal. There are various ways to characterize filters. Linear filters satisfy the superposition principle, i.e. if an input is a weighted linear combination of different signals, the output is a weighted linear combination of the corresponding output signals.
A causal filter uses only previous samples of the output signals. A non-causal filter can be changed into a causal filter by adding a delay to it. A time-invariant filter has constant properties over time. A stable filter produces an output that converges to a constant value with time, or remains bounded within a finite interval. An unstable filter can produce an output that grows without bounds, with bounded or zero input. A finite impulse response filter uses only the input signals, while an infinite impulse response filter uses both the input signal and previous samples of the output signal. FIR filters are always stable. A filter can be represented by a block diagram, which can be used to derive a sample processing algorithm to implement the filter with hardware instructions. A filter may be described as a difference equation, a collection of zeros and poles or an impulse response or step response; the output of a linear digital filter to any given input may be calculated by convolving the input signal with the impulse response.
Signals are converted from time or space domain to the frequency domain through use of the Fourier transform. The Fourier transform converts the time or space information to a magnitude and phase component of each frequency. With some applications, how the phase varies with frequency can be a significant consideration. Where phase is unimportant the Fourier transform is converted to the power spectrum, the magnitude of each frequency component squared; the most common purpose for analysis of signals in the frequency domain is analysis of signal properties. The engineer can study the spectrum to determine which frequencies are present in the input signal and which are missing. Frequency domain analysis is called spectrum- or spectral analysis. Filtering in non-realtime work can be achieved in the frequency domain, applying the filter and converting back to the time domain; this can be an efficient implementation and can g
Image quality
Image quality can refer to the level of accuracy in which different imaging systems capture, store, compress and display the signals that form an image. Another definition refers to image quality as "the weighted combination of all of the visually significant attributes of an image"; the difference between the two definitions is that one focus on the characteristics of signal processing in different imaging systems and the latter on the perceptual assessments that make an image pleasant for human viewers. Image quality should not be mistaken with image fidelity. Image fidelity refers to the ability of a process to render a given copy in a perceptually similar way to the original, i.e. through a digitization or conversion process from analog media to digital image. The process of determining the level of accuracy is called Image Quality Assessment. Image quality assessment is part of the quality of experience measures. Image quality can be assessed using two methods: objective. Subjective methods are based on the perceptual assessment of a human viewer about the attributes of an image or set of images, while objective methods are based on computational models that can predict perceptual image quality.
Objective and subjective methods aren't consistent or accurate between each other: a human viewer might perceive stark differences in quality in a set of images where a computer algorithm might not. Subjective methods are costly, require a large number of people, are impossible to automate in real-time. Therefore, the goal of image quality assessment research is to design algorithms for objective assessment that are consistent with subjective assessments; the development of such algorithms has a lot of potential applications. They can be used to monitor image quality in control quality systems, to benchmark image processing systems and algorithms and to optimize imaging systems; the image formation process is affected by several distortions between the moment in which the signals travel through to and reach the capture surface, the device or mean in which signals are displayed. Although optical aberrations can cause great distorsions in image quality, they are not part of the field of Image Quality Assessment.
Optical aberrations caused by lenses belong to the optics area and not to the signal processing areas. In an ideal model, there's no quality loss between the emission of the signal and the surface in which the signal is being captured on. For example, a digital image is formed by electromagnetic radiation or other waves as they pass through or reflect off objects; that information is captured and converted into digital signals by an image sensor. The sensor, has nonidealities that limit its performance. Image quality can be assessed using subjective methods. In the objective method, image quality assessments are performed by different algorithms that analyze the distortions and degradations introduced in an image. Subjective image quality assessments are a method based on the way in which humans experience or perceive image quality. Objective and subjective methods of quality assessment don't correlate with each other. An algorithm might have a similar value for an image and its altered or degraded versions, while a subjective method might perceive a stark contrast in quality for the same image and its versions.
See main article: Subjective video quality Subjective methods for image quality assessment belong to the larger area of psychophysics research, a field that studies the relationship between physical stimulus and human perceptions. A subjective IQA method will consist on applying mean opinion score techniques, where a number of viewers rate their opinions based on their perceptions of image quality; these opinions are afterwards mapped onto numerical values. These methods can be classified depending on the availability of the source and test images: Single-stimulus: the viewer only has the test image and is not aware of the source image. Double-stimulus: the viewer has both the source and test image. Since visual perception can be affected by environmental and viewing conditions, the International Telecommunications Union produced a set of recommendations for standardized testing methods for subjective image quality assessment. Wang & Bovic classify the objective methods with the following criteria: the availability of an original image.
Keelan classifies the methods based on direct experimental measurements. Full-reference methods – FR metrics try to assess the quality of a test image by comparing it with a reference image, assumed to have perfect quality, e.g. the original of an image versus a JPEG-compressed version of the image. Reduced-reference methods – RR metrics assess the quality of a test and reference image based on a comparison of features extracted from both images. No-reference methods – NR metrics try to assess the quality of a test image without any reference to the original one. Image quality metrics can be classified in terms of measuring only one specific type of degradation, or taking into account all possible signal distortions, that is, multiple kinds of artifacts. Sharpness determines the amount of detail. System sharpness is affected by the sensor. In the field, sharpness is affected by camera shake, focus accuracy, atmospheric d
Web browser
A web browser is a software application for accessing information on the World Wide Web. Each individual web page and video is identified by a distinct Uniform Resource Locator, enabling browsers to retrieve these resources from a web server and display them on the user's device. A web browser is not the same thing as a search engine, though the two are confused. For a user, a search engine is just a website, such as google.com, that stores searchable data about other websites. But to connect to a website's server and display its web pages, a user needs to have a web browser installed on their device; the most popular browsers are Chrome, Safari, Internet Explorer, Edge. The first web browser, called WorldWideWeb, was invented in 1990 by Sir Tim Berners-Lee, he recruited Nicola Pellow to write the Line Mode Browser, which displayed web pages on dumb terminals. 1993 was a landmark year with the release of Mosaic, credited as "the world's first popular browser". Its innovative graphical interface made the World Wide Web system easy to use and thus more accessible to the average person.
This, in turn, sparked the Internet boom of the 1990s when the Web grew at a rapid rate. Marc Andreessen, the leader of the Mosaic team, soon started his own company, which released the Mosaic-influenced Netscape Navigator in 1994. Navigator became the most popular browser. Microsoft debuted Internet Explorer in 1995. Microsoft was able to gain a dominant position for two reasons: it bundled Internet Explorer with its popular Microsoft Windows operating system and did so as freeware with no restrictions on usage; the market share of Internet Explorer peaked at over 95% in 2002. In 1998, desperate to remain competitive, Netscape launched what would become the Mozilla Foundation to create a new browser using the open source software model; this work evolved into Firefox, first released by Mozilla in 2004. Firefox reached a 28% market share in 2011. Apple released its Safari browser in 2003, it remains the dominant browser on Apple platforms. The last major entrant to the browser market was Google, its Chrome browser, which debuted in 2008, has been a huge success.
It took market share from Internet Explorer and became the most popular browser in 2012. Chrome has remained dominant since. In terms of technology, browsers have expanded their HTML, CSS, JavaScript, multimedia capabilities since the 1990s. One reason has been to enable more sophisticated websites, such as web applications. Another factor is the significant increase of broadband connectivity, which enables people to access data-intensive web content, such as YouTube streaming, not possible during the era of dial-up modems; the purpose of a web browser is to fetch information resources from the Web and display them on a user's device. This process begins. All URLs on the Web start with either http: or https: which means the browser will retrieve them with the Hypertext Transfer Protocol. In the case of https:, the communication between the browser and the web server is encrypted for the purposes of security and privacy. Another URL prefix is file:, used to display local files stored on the user's device.
Once a web page has been retrieved, the browser's rendering engine displays it on the user's device. This includes video formats supported by the browser. Web pages contain hyperlinks to other pages and resources; each link contains a URL, when it is clicked, the browser navigates to the new resource. Thus the process of bringing content to the user begins again. To implement all of this, modern browsers are a combination of numerous software components. Web browsers can be configured with a built-in menu. Depending on the browser, the menu may be named Options, or Preferences; the menu has different types of settings. For example, users can change their home default search engine, they can change default web page colors and fonts. Various network connectivity and privacy settings are usually available. During the course of browsing, cookies received from various websites are stored by the browser; some of them contain login credentials or site preferences. However, others are used for tracking user behavior over long periods of time, so browsers provide settings for removing cookies when exiting the browser.
Finer-grained management of cookies requires a browser extension. The most popular browsers have a number of features in common, they allow users to browse in a private mode. They can be customized with extensions, some of them provide a sync service. Most browsers have these user interface features: Allow the user to open multiple pages at the same time, either in different browser windows or in different tabs of the same window. Back and forward buttons to go back to the previous page forward to the next one. A refresh or reload button to reload the current page. A stop button to cancel loading the page. A home button to return to the user's home page. An address bar to display it. A search bar to input terms into a search engine. There are niche browsers with distinct features. One example is text-only browsers that can benefit people with slow Internet connections or those with visual impairments. Mobile browser List of web browsers Comparison of web browsers Media related to Web browsers at Wikimedia Commons
Peak signal-to-noise ratio
Peak signal-to-noise ratio abbreviated PSNR, is an engineering term for the ratio between the maximum possible power of a signal and the power of corrupting noise that affects the fidelity of its representation. Because many signals have a wide dynamic range, PSNR is expressed in terms of the logarithmic decibel scale. PSNR is most defined via the mean squared error. Given a noise-free m×n monochrome image I and its noisy approximation K, MSE is defined as: M S E = 1 m n ∑ i = 0 m − 1 ∑ j = 0 n − 1 2 The PSNR is defined as: P S N R = 10 ⋅ log 10 = 20 ⋅ log 10 = 20 ⋅ log 10 − 10 ⋅ log 10 Here, MAXI is the maximum possible pixel value of the image; when the pixels are represented using 8 bits per sample, this is 255. More when samples are represented using linear PCM with B bits per sample, MAXI is 2B−1. For color images with three RGB values per pixel, the definition of PSNR is the same except the MSE is the sum over all squared value differences divided by image size and by three. Alternately, for color images the image is converted to a different color space and PSNR is reported against each channel of that color space, e.g. YCbCr or HSL.
PSNR is most used to measure the quality of reconstruction of lossy compression codecs. The signal in this case is the original data, the noise is the error introduced by compression; when comparing compression codecs, PSNR is an approximation to human perception of reconstruction quality. Typical values for the PSNR in lossy image and video compression are between 30 and 50 dB, provided the bit depth is 8 bits, where higher is better. For 16-bit data typical values for the PSNR are between 60 and 80 dB. Acceptable values for wireless transmission quality loss are considered to be about 20 dB to 25 dB. In the absence of noise, the two images I and K are identical, thus the MSE is zero. In this case the PSNR is infinite. Although a higher PSNR indicates that the reconstruction is of higher quality, in some cases it may not. One has to be careful with the range of validity of this metric. PSNR has been shown to perform poorly compared to other quality metrics when it comes to estimating the quality of images and videos as perceived by humans.
PSNR-HVS is an extension of PSNR that incorporates properties of the human visual system such as contrast perception. PSNR-HVS-M improves on PSNR-HVS by additionally taking into account visual masking. In a 2007 study, it delivered better approximations of human visual quality judgements than PSNR and SSIM by large margin, it was shown to have a distinct advantage over DCTune and PSNR-HVS. Data compression ratio Perceptual Evaluation of Video Quality Signal-to-noise ratio Structural similarity index Subjective video quality Video quality
Nyquist–Shannon sampling theorem
In the field of digital signal processing, the sampling theorem is a fundamental bridge between continuous-time signals and discrete-time signals. It establishes a sufficient condition for a sample rate that permits a discrete sequence of samples to capture all the information from a continuous-time signal of finite bandwidth. Speaking, the theorem only applies to a class of mathematical functions having a Fourier transform, zero outside of a finite region of frequencies. Intuitively we expect that when one reduces a continuous function to a discrete sequence and interpolates back to a continuous function, the fidelity of the result depends on the density of the original samples; the sampling theorem introduces the concept of a sample rate, sufficient for perfect fidelity for the class of functions that are bandlimited to a given bandwidth, such that no actual information is lost in the sampling process. It expresses the sufficient sample rate in terms of the bandwidth for the class of functions.
The theorem leads to a formula for reconstructing the original continuous-time function from the samples. Perfect reconstruction may still be possible when the sample-rate criterion is not satisfied, provided other constraints on the signal are known. In some cases, utilizing additional constraints allows for approximate reconstructions; the fidelity of these reconstructions can be quantified utilizing Bochner's theorem. The name Nyquist–Shannon sampling theorem honors Harry Nyquist and Claude Shannon; the theorem was discovered independently by E. T. Whittaker, by Vladimir Kotelnikov, by others, it is thus known by the names Nyquist–Shannon–Kotelnikov, Whittaker–Shannon–Kotelnikov, Whittaker–Nyquist–Kotelnikov–Shannon, cardinal theorem of interpolation. Sampling is a process of converting a signal into a numeric sequence. Shannon's version of the theorem states: If a function x contains no frequencies higher than B hertz, it is determined by giving its ordinates at a series of points spaced 1 / seconds apart.
A sufficient sample-rate is therefore anything larger than 2 B samples per second. Equivalently, for a given sample rate f s, perfect reconstruction is guaranteed possible for a bandlimit B < f s / 2. When the bandlimit is too high, the reconstruction exhibits imperfections known as aliasing. Modern statements of the theorem are sometimes careful to explicitly state that x must contain no sinusoidal component at frequency B, or that B must be less than ½ the sample rate; the threshold 2 B is called the Nyquist rate and is an attribute of the continuous-time input x to be sampled. The sample rate must exceed the Nyquist rate for the samples to suffice to represent x; the threshold fs/2 is an attribute of the sampling equipment. All meaningful frequency components of the properly sampled x exist below the Nyquist frequency; the condition described by these inequalities is called the Nyquist criterion, or sometimes the Raabe condition. The theorem is applicable to functions of other domains, such as space, in the case of a digitized image.
The only change, in the case of other domains, is the units of measure applied to t, fs, B. The symbol T = 1/fs is customarily used to represent the interval between samples and is called the sample period or sampling interval, and the samples of function x are denoted by x = x, for all integer values of n. A mathematically ideal way to interpolate the sequence involves the use of sinc functions; each sample in the sequence is replaced by a sinc function, centered on the time axis at the original location of the sample, nT, with the amplitude of the sinc function scaled to the sample value, x. Subsequently, the sinc functions are summed into a continuous function. A mathematically equivalent method is to convolve one sinc function with a series of Dirac delta pulses, weighted by the sample values. Neither method is numerically practical. Instead, some type of approximation of the sinc functions, finite in length, is used; the imperfections attributable to the approximation are known as interpolation error.
Practical digital-to-analog converters produce neither scaled and delayed sinc functions, nor ideal Dirac pulses. Instead they produce a piecewise-constant sequence of scaled and delayed rectangular pulses followed by an "anti-aliasing filter" to clean up spurious high-frequency content; when x is a function with a Fourier transform X: X ≜ ∫ − ∞ ∞ x e − i 2 π f t d t, {\displaystyle X\ \triangleq \ \int _^x\ e^\ {\rm {
Game engine
A game engine is a software-development environment designed for people to build video games. Developers use game engines to construct games for consoles, mobile devices, personal computers; the core functionality provided by a game engine includes a rendering engine for 2D or 3D graphics, a physics engine or collision detection, scripting, artificial intelligence, streaming, memory management, localization support, scene graph, may include video support for cinematics. Implementers economize on the process of game development by reusing/adapting, in large part, the same game engine to produce different games or to aid in porting games to multiple platforms. In many cases game engines provide a suite of visual development tools in addition to reusable software components; these tools are provided in an integrated development environment to enable simplified, rapid development of games in a data-driven manner. Game engine developers attempt to "pre-invent the wheel" by developing robust software suites which include many elements a game developer may need to build a game.
Most game engine suites provide facilities that ease development, such as graphics, physics and AI functions. These game engines are sometimes called "middleware" because, as with the business sense of the term, they provide a flexible and reusable software platform which provides all the core functionality needed, right out of the box, to develop a game application while reducing costs and time-to-market — all critical factors in the competitive video game industry; as of 2001, Gamebryo, JMonkeyEngine and RenderWare were such used middleware programs. Like other types of middleware, game engines provide platform abstraction, allowing the same game to be run on various platforms including game consoles and personal computers with few, if any, changes made to the game source code. Game engines are designed with a component-based architecture that allows specific systems in the engine to be replaced or extended with more specialized game middleware components; some game engines are designed as a series of loosely connected game middleware components that can be selectively combined to create a custom engine, instead of the more common approach of extending or customizing a flexible integrated product.
However extensibility is achieved, it remains a high priority for game engines due to the wide variety of uses for which they are applied. Despite the specificity of the name, game engines are used for other kinds of interactive applications with real-time graphical needs such as marketing demos, architectural visualizations, training simulations, modeling environments; some game engines only provide real-time 3D rendering capabilities instead of the wide range of functionality needed by games. These engines rely upon the game developer to implement the rest of this functionality or assemble it from other game middleware components; these types of engines are referred to as a "graphics engine", "rendering engine", or "3D engine" instead of the more encompassing term "game engine". This terminology is inconsistently used as many full-featured 3D game engines are referred to as "3D engines". A few examples of graphics engines are: Crystal Space, Genesis3D, Irrlicht, OGRE, RealmForge, Truevision3D, Vision Engine.
Modern game or graphics engines provide a scene graph, an object-oriented representation of the 3D game world which simplifies game design and can be used for more efficient rendering of vast virtual worlds. As technology ages, the components of an engine may become outdated or insufficient for the requirements of a given project. Since the complexity of programming an new engine may result in unwanted delays, a development team may elect to update their existing engine with newer functionality or components; such a framework is composed of a multitude of different components. The actual game logic has to be implemented by some algorithms, it is distinct from sound or input work. The rendering engine generates animated 3D graphics by any of a number of methods. Instead of being programmed and compiled to be executed on the CPU or GPU directly, most rendering engines are built upon one or multiple rendering application programming interfaces, such as Direct3D, OpenGL, or Vulkan which provide a software abstraction of the graphics processing unit.
Low-level libraries such as DirectX, Simple DirectMedia Layer, OpenGL are commonly used in games as they provide hardware-independent access to other computer hardware such as input devices, network cards, sound cards. Before hardware-accelerated 3D graphics, software renderers had been used. Software rendering is still used in some modeling tools or for still-rendered images when visual accuracy is valued over real-time performance or when the computer hardware does not meet needs such as shader support. With the advent of hardware accelerated physics processing, various physics APIs such as PAL and the physics extensions of COLLADA became available to provide a software abstraction of the physics processing unit of different middleware providers and console platforms. Game engines can be written in any programming language like C++, C or Java, though each language is structurally different and may provide different levels of access to specific functions; the audio engine is the component which consists of algorithms related to the loading and output of sound through the client's speaker system.
At a minimum i
Lanczos resampling
Lanczos filtering and Lanczos resampling are two applications of a mathematical formula. It can be used as a low-pass filter or used to smoothly interpolate the value of a digital signal between its samples. In the latter case it maps each sample of the given signal to a translated and scaled copy of the Lanczos kernel, a sinc function windowed by the central lobe of a second, sinc function; the sum of these translated and scaled kernels is evaluated at the desired points. Lanczos resampling is used to increase the sampling rate of a digital signal, or to shift it by a fraction of the sampling interval, it is used for multivariate interpolation, for example to resize or rotate a digital image. It has been considered the "best compromise" among several simple filters for this purpose; the filter is named after Cornelius Lanczos. The effect of each input sample on the interpolated values is defined by the filter's reconstruction kernel L, called the Lanczos kernel, it is the normalized sinc function sinc, windowed by the Lanczos window, or sinc window, the central lobe of a horizontally stretched sinc function sinc for −a ≤ x ≤ a.
L = { sinc sinc if − a < x < a, 0 otherwise. Equivalently, L = { 1 if x = 0, a sin sin π 2 x 2 if − a ≤ x < a and x ≠ 0, 0 otherwise. The parameter a is a positive integer 2 or 3, which determines the size of the kernel; the Lanczos kernel has 2a − 1 lobes: a positive one at the center, a − 1 alternating negative and positive lobes on each side. Given a one-dimensional signal with samples si, for integer values of i, the value S interpolated at an arbitrary real argument x is obtained by the discrete convolution of those samples with the Lanczos kernel: S = ∑ i = ⌊ x ⌋ − a + 1 ⌊ x ⌋ + a s i L, where a is the filter size parameter, ⌊ x ⌋ is the floor function; the bounds of this sum are such. As long as the parameter a is a positive integer, the Lanczos kernel is continuous everywhere, its derivative is defined and continuous everywhere. Therefore, the reconstructed signal S too will be continuous, with continuous derivative; the Lanczos kernel is zero at every integer argument x, except at x = 0, where it has value 1.
Therefore, the reconstructed signal interpolates the given samples: we will have S = si for every integer argument x = i. Lanczos filter's kernel in two dimensions is L = L L; the theoretically optimal reconstruction filter for band-limited signals is the sinc filter, which has infinite support. The Lanczos filter is one of many practical approximations of the sinc filter; each interpolated value is the weighted sum of 2a consecutive input samples. Thus, by varying the 2a parameter one may trade computation speed for improved frequency response; the parameter allows one to choose between a smoother interpolation or a preservation of sharp transients in the data. For image processing, the trade-off is between the reduction of aliasing artefacts and the preservation of sharp edges; as with any such processing, there are no results for the borders of the image. Increasing the length of the kernel increases the cropping of the edges of the image; the Lanczos filter has been compared with other interpolation meth
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