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2D Filters : ウィキペディア英語版
2D Filters

Two dimensional filters have seen substantial development effort due to their importance and large applicability across several domains. In the 2-D case the situation is quite different from 1-D case, because the multi-dimensional polynomials can't be factored in generally. This means that an arbitrary transfer function can generally not be manipulated into a form required by a particular implementation. The input-output relationship of a 2-D IIR filter obeys a constant-coefficient linear partial difference equation from which the value of an output sample can be computed using the input samples and previously computed output samples. Because the values of the output samples are fed back, the 2-D filter, like its 1-D counterpart, can be unstable.
== Motivation & Applications ==
Due to the rapid development of information science and computing technology, the theory of digital filters design and application has achieved leap-forward development. We encounter a variety of signals in real-life, such as broadcasting signals, television signals, radar signals, mobile phone signals, navigation signals, radio astronomy signal, biomedical signals, control signals, weather signal, seismic signal, mechanical vibration signal, remote sensing and telemetry signals, etc. Most of these signals are analog signals and just a small portion of them are digital signals. The analog signals are continuous function of the independent variables, which can be one-dimensional, two-dimensional or multidimensional. In most cases, the variable of one-dimensional analog signals are time. After the time sampling and discretization of magnitude, such analog signal will become a one-dimensional digital signal. The resulting digital signal can be represented by a discrete sequence. For example, one common signal is voice signal. An example of a two-dimensional signal is an image. A filter is a system that can transform a signal into another signal. Examples of such transformation include smoothing the signal for noise removal, removing frequency components from a signal and amplifying frequency components for signal enhancement. The design and implementation of filter is an important branch in signal analysis and processing technology. Filters also play a main role in signal acquisition, transmission, processing and exchange.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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