Image Filter End Terminations
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Image Filter End Terminations
Filters designed using the image impedance methodology suffer from a peculiar flaw in the theory. The predicted characteristics of the filter are calculated assuming that the filter is terminated with its own image impedances at each end. This will not usually be the case; the filter will be terminated with fixed resistances. This causes the filter response to deviate from the theoretical. This article explains how the effects of image filter end terminations can be taken into account. Generally, the effect of the terminations is to cause a rounding of the frequency response at cut-off. The image method predicts a sharp discontinuity in the slope of the response at cut-off which is not realised in practice, although a well designed image filter may get close to this. Another prediction of the image method is zero loss in the passband (assuming ideal lossless components). Again, this cannot be achieved in practice because reflections from the end terminations always cause some ...
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Filter (signal Processing)
In signal processing, a filter is a device or process that removes some unwanted components or features from a signal. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal. Most often, this means removing some frequencies or frequency bands. However, filters do not exclusively act in the frequency domain; especially in the field of image processing many other targets for filtering exist. Correlations can be removed for certain frequency components and not for others without having to act in the frequency domain. Filters are widely used in electronics and telecommunication, in radio, television, audio recording, radar, control systems, music synthesis, image processing, and computer graphics. There are many different bases of classifying filters and these overlap in many different ways; there is no simple hierarchical classification. Filters may be: * non-linear or linear * time-variant ...
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Dual Impedance
Dual impedance and dual network are terms used in electronic network analysis. The dual of an impedance Z is its reciprocal, or algebraic inverse Z'=\frac. For this reason the dual impedance is also called the inverse impedance. Another way of stating this is that the dual of Z is the admittance Y'=Z. The dual of a network is the network whose impedances are the duals of the original impedances. In the case of a black-box network with multiple ports, the impedance looking into each port must be the dual of the impedance of the corresponding port of the dual network. This is consistent with the general notion duality of electric circuits, where the voltage and current are interchanged, etc., since Z=\frac yields Z'=\frac __TOC__ Scaled and normalised duals In physical units, the dual is taken with respect to some nominal or characteristic impedance. To do this, Z and Z' are scaled to the nominal impedance Z0 so that : \frac=\frac Z0 is usually taken to be a purely rea ...
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Filter Theory
Filter design is the process of designing a signal processing filter that satisfies a set of requirements, some of which may be conflicting. The purpose is to find a realization of the filter that meets each of the requirements to a sufficient degree to make it useful. The filter design process can be described as an optimization problem where each requirement contributes to an error function that should be minimized. Certain parts of the design process can be automated, but normally an experienced electrical engineer is needed to get a good result. The design of digital filters is a deceptively complex topic. Although filters are easily understood and calculated, the practical challenges of their design and implementation are significant and are the subject of advanced research. Typical design requirements Typical requirements which are considered in the design process are: * The filter should have a specific frequency response * The filter should have a specific phase sh ...
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Image Impedance Filters
An image is a visual representation of something. It can be two-dimensional, three-dimensional, or somehow otherwise feed into the visual system to convey information. An image can be an artifact, such as a photograph or other two-dimensional picture, that resembles a subject. In the context of signal processing, an image is a distributed amplitude of color(s). In optics, the term “image” may refer specifically to a 2D image. An image does not have to use the entire visual system to be a visual representation. A popular example of this is of a greyscale image, which uses the visual system's sensitivity to brightness across all wavelengths, without taking into account different colors. A black and white visual representation of something is still an image, even though it does not make full use of the visual system's capabilities. Images are typically still, but in some cases can be moving or animated. Characteristics Images may be two or three-dimensional, such as a pho ...
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Linear Filters
Linear filters process time-varying input signals to produce output signals, subject to the constraint of linearity. In most cases these linear filters are also time invariant (or shift invariant) in which case they can be analyzed exactly using LTI ("linear time-invariant") system theory revealing their transfer functions in the frequency domain and their impulse responses in the time domain. Real-time implementations of such linear signal processing filters in the time domain are inevitably causal, an additional constraint on their transfer functions. An analog electronic circuit consisting only of linear components (resistors, capacitors, inductors, and linear amplifiers) will necessarily fall in this category, as will comparable mechanical systems or digital signal processing systems containing only linear elements. Since linear time-invariant filters can be completely characterized by their response to sinusoids of different frequencies (their frequency response), they are s ...
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Prototype Filter
Prototype filters are electronic filter designs that are used as a template to produce a modified filter design for a particular application. They are an example of a nondimensionalised design from which the desired filter can be scaled or transformed. They are most often seen in regard to electronic filters and especially linear analogue passive filters. However, in principle, the method can be applied to any kind of linear filter or signal processing, including mechanical, acoustic and optical filters. Filters are required to operate at many different frequencies, impedances and bandwidths. The utility of a prototype filter comes from the property that all these other filters can be derived from it by applying a scaling factor to the components of the prototype. The filter design need thus only be carried out once in full, with other filters being obtained by simply applying a scaling factor. Especially useful is the ability to transform from one bandform to another. In t ...
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Composite Image Filter
A composite image filter is an electronic filter consisting of multiple image filter sections of two or more different types. The image method of filter design determines the properties of filter sections by calculating the properties they have in an infinite chain of such sections. In this, the analysis parallels transmission line theory on which it is based. Filters designed by this method are called ''image parameter filters'', or just ''image filters''. An important parameter of image filters is their image impedance, the impedance of an infinite chain of identical sections. The basic sections are arranged into a ladder network of several sections, the number of sections required is mostly determined by the amount of stopband rejection required. In its simplest form, the filter can consist entirely of identical sections. However, it is more usual to use a composite filter of two or three different types of section to improve different parameters best addressed by a pa ...
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T Filter Response, Component Due To Terminations
T, or t, is the twentieth letter in the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''tee'' (pronounced ), plural ''tees''. It is derived from the Semitic Taw 𐤕 of the Phoenician and Paleo-Hebrew script (Aramaic and Hebrew Taw ת/𐡕/, Syriac Taw ܬ, and Arabic ت Tāʼ) via the Greek letter τ (tau). In English, it is most commonly used to represent the voiceless alveolar plosive, a sound it also denotes in the International Phonetic Alphabet. It is the most commonly used consonant and the second most commonly used letter in English-language texts. History ''Taw'' was the last letter of the Western Semitic and Hebrew alphabets. The sound value of Semitic ''Taw'', Greek alphabet Tαυ (''Tau''), Old Italic and Latin T has remained fairly constant, representing in each of these; and it has also kept its original basic shape in most of these alphabets. Use in wr ...
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Theoretical T Filter Response
A theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may be scientific, belong to a non-scientific discipline, or no discipline at all. Depending on the context, a theory's assertions might, for example, include generalized explanations of how nature works. The word has its roots in ancient Greek, but in modern use it has taken on several related meanings. In modern science, the term "theory" refers to scientific theories, a well-confirmed type of explanation of nature, made in a way consistent with the scientific method, and fulfilling the criteria required by modern science. Such theories are described in such a way that scientific tests should be able to provide empirical support for it, or empirical contradiction ("falsify") of it. Scientific theories are the most reliable, rigorous, and compreh ...
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Antimetric (electrical Networks)
An antimetric electrical network is an electrical network that exhibits anti- symmetrical electrical properties. The term is often encountered in filter theory, but it applies to general electrical network analysis. Antimetric is the diametrical opposite of symmetric; it does not merely mean "asymmetric" (i.e., "lacking symmetry"). It is possible for networks to be symmetric or antimetric in their electrical properties without being physically or topologically symmetric or antimetric. Definition References to symmetry and antimetry of a network usually refer to the input impedancesinput impedance. The input impedance of a port is the impedance measured across that network port with nothing connected to it externally and all other ports terminated with a defined impedance. of a two-port network when correctly terminated."correctly terminated". This will most usually mean termination with the system nominal impedance which, in turn, is usually chosen to equal the nominal chara ...
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