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Full Scale
In electronics and signal processing, full scale represents the maximum amplitude a system can represent. In digital systems, a signal is said to be at digital full scale when its magnitude has reached the maximum representable value. Once a signal has reached digital full scale, all headroom has been utilized, and any further increase in amplitude will result in an error known as clipping. The amplitude of a digital signal can be represented in percent; full scale; or decibels, full scale (dBFS). In analog systems, full scale may be defined by the maximum voltage available, or the maximum deflection (full scale deflection or FSD) or indication of an analog instrument such as a moving coil meter or galvanometer. Binary representation Since binary integer representation range is asymmetrical, full scale is defined using the maximum positive value that can be represented. For example, 16-bit PCM audio is centered on the value 0, and can contain values from −32,768 to +32, ...
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Electronics
Electronics is a scientific and engineering discipline that studies and applies the principles of physics to design, create, and operate devices that manipulate electrons and other Electric charge, electrically charged particles. It is a subfield of physics and electrical engineering which uses Passivity (engineering), active devices such as transistors, diodes, and integrated circuits to control and amplify the flow of electric current and to convert it from one form to another, such as from alternating current (AC) to direct current (DC) or from analog signal, analog signals to digital signal, digital signals. Electronic devices have significantly influenced the development of many aspects of modern society, such as telecommunications, entertainment, education, health care, industry, and security. The main driving force behind the advancement of electronics is the semiconductor industry, which continually produces ever-more sophisticated electronic devices and circuits in respo ...
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Floating-point Arithmetic
In computing, floating-point arithmetic (FP) is arithmetic on subsets of real numbers formed by a ''significand'' (a Sign (mathematics), signed sequence of a fixed number of digits in some Radix, base) multiplied by an integer power of that base. Numbers of this form are called floating-point numbers. For example, the number 2469/200 is a floating-point number in base ten with five digits: 2469/200 = 12.345 = \! \underbrace_\text \! \times \! \underbrace_\text\!\!\!\!\!\!\!\overbrace^ However, 7716/625 = 12.3456 is not a floating-point number in base ten with five digits—it needs six digits. The nearest floating-point number with only five digits is 12.346. And 1/3 = 0.3333… is not a floating-point number in base ten with any finite number of digits. In practice, most floating-point systems use Binary number, base two, though base ten (decimal floating point) is also common. Floating-point arithmetic operations, such as addition and division, approximate the correspond ...
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Audio Normalization
Audio normalization is the application of a constant amount of gain to an audio recording to bring the amplitude to a target level (the norm). Because the same amount of gain is applied across the entire recording, the signal-to-noise ratio and relative dynamics are unchanged. Normalization is one of the functions commonly provided by a digital audio workstation. Two principal types of audio normalization exist. Peak normalization adjusts the recording based on the highest signal level present in the recording. Loudness normalization adjusts the recording based on perceived loudness. Normalization differs from dynamic range compression, which applies varying levels of gain over a recording to fit the level within a minimum and maximum range. Normalization adjusts the gain by a constant value across the entire recording. Peak normalization One type of normalization is peak normalization, wherein the gain is changed to bring the highest PCM sample value or analog signal peak ...
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Nyquist Theorem
Nyquist may refer to: * Nyquist (surname) * Nyquist (horse), winner of the 2016 Kentucky Derby * Nyquist (programming language), computer programming language for sound synthesis and music composition See also *Johnson–Nyquist noise, thermal noise *Nyquist stability criterion, in control theory **Nyquist plot, signal processing and electronic feedback *Nyquist–Shannon sampling theorem, fundamental result in the field of information theory **Nyquist frequency, digital signal processing **Nyquist rate, telecommunication theory **Nyquist ISI criterion In communications, the Nyquist ISI criterion describes the conditions which, when satisfied by a communication channel (including responses of transmit and receive filters), result in no intersymbol interference or ISI. It provides a method for ..., telecommunication theory * 6625 Nyquist, a main-belt asteroid * Nyquist filter, a filter used in television systems * Enquist * Nyqvist (other) {{disambiguation ...
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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 ...
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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. 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. 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. Due to the complexity ...
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Ringing Artifacts
In signal processing, particularly digital image processing, ringing artifacts are Artifact (error), artifacts that appear as spurious signals near sharp transitions in a signal. Visually, they appear as bands or "ghosts" near edges; audibly, they appear as "echos" near Transient (acoustics), transients, particularly sounds from percussion instruments; most noticeable are the pre-echos. The term "ringing" is because the output signal oscillates at a fading rate around a sharp transition in the input, similar to a Bell (instrument), bell after being struck. As with other artifacts, their minimization is a criterion in filter design. Introduction The main cause of ringing artifacts is due to a signal being bandlimited (specifically, not having high frequencies) or passed through a low-pass filter; this is the frequency domain description. In terms of the time domain, the cause of this type of ringing is the ripples in the sinc function,, section I.6, Enhancement: Frequency Doma ...
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Reconstruction Filter
In a mixed-signal system ( analog and digital), a reconstruction filter, sometimes called an anti-imaging filter, is used to construct a smooth analog signal from a digital input, as in the case of a digital to analog converter ( DAC) or other sampled data output device. Sampled data reconstruction filters The sampling theorem describes why the input of an ADC requires a low-pass analog electronic filter, called the anti-aliasing filter: the sampled ''input'' signal must be bandlimited to prevent aliasing (here meaning waves of higher frequency being ''recorded'' as a lower frequency). For the same reason, the output of a DAC requires a low-pass analog filter, called a reconstruction filter - because the ''output'' signal must be bandlimited, to prevent imaging (meaning Fourier coefficients being reconstructed as spurious high-frequency 'mirrors'). This is an implementation of the Whittaker–Shannon interpolation formula. Ideally, both filters should be brickwall filters, ...
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Sample Rate Conversion
Sample-rate conversion, sampling-frequency conversion or resampling is the process of changing the sampling rate or sampling frequency of a discrete signal to obtain a new discrete representation of the underlying continuous signal. Application areas include image scaling and audio/visual systems, where different sampling rates may be used for engineering, economic, or historical reasons. For example, Compact Disc Digital Audio and Digital Audio Tape systems use different sampling rates, and American television, European television, and movies all use different frame rates. Sample-rate conversion prevents changes in speed and pitch that would otherwise occur when transferring recorded material between such systems. More specific types of resampling include: ''upsampling'' or ''upscaling''; ''downsampling'', ''downscaling'', or ''decimation''; and ''interpolation''. The term multi-rate digital signal processing is sometimes used to refer to systems that incorporate sample-rate co ...
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Anti-aliasing Filter
An anti-aliasing filter (AAF) is a filter used before a signal sampler to restrict the bandwidth of a signal to satisfy the Nyquist–Shannon sampling theorem over the band of interest. Since the theorem states that unambiguous reconstruction of the signal from its samples is possible when the power of frequencies above the Nyquist frequency is zero, a brick wall filter is an idealized but impractical AAF. A practical AAF makes a trade off between reduced bandwidth and increased aliasing. A practical anti-aliasing filter will typically permit some aliasing to occur or attenuate or otherwise distort some in-band frequencies close to the Nyquist limit. For this reason, many practical systems sample higher than would be theoretically required by a perfect AAF in order to ensure that all frequencies of interest can be reconstructed, a practice called oversampling. Optical applications In the case of optical image sampling, as by image sensors in digital cameras, the anti ...
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Floating-point Arithmetic
In computing, floating-point arithmetic (FP) is arithmetic on subsets of real numbers formed by a ''significand'' (a Sign (mathematics), signed sequence of a fixed number of digits in some Radix, base) multiplied by an integer power of that base. Numbers of this form are called floating-point numbers. For example, the number 2469/200 is a floating-point number in base ten with five digits: 2469/200 = 12.345 = \! \underbrace_\text \! \times \! \underbrace_\text\!\!\!\!\!\!\!\overbrace^ However, 7716/625 = 12.3456 is not a floating-point number in base ten with five digits—it needs six digits. The nearest floating-point number with only five digits is 12.346. And 1/3 = 0.3333… is not a floating-point number in base ten with any finite number of digits. In practice, most floating-point systems use Binary number, base two, though base ten (decimal floating point) is also common. Floating-point arithmetic operations, such as addition and division, approximate the correspond ...
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Signal Processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as audio signal processing, sound, image processing, images, Scalar potential, potential fields, Seismic tomography, seismic signals, Altimeter, altimetry processing, and scientific measurements. Signal processing techniques are used to optimize transmissions, Data storage, digital storage efficiency, correcting distorted signals, improve subjective video quality, and to detect or pinpoint components of interest in a measured signal. History According to Alan V. Oppenheim and Ronald W. Schafer, the principles of signal processing can be found in the classical numerical analysis techniques of the 17th century. They further state that the digital refinement of these techniques can be found in the digital control systems of the 1940s and 1950s. In 1948, Claude Shannon wrote the influential paper "A Mathematical Theory of Communication" which was publis ...
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