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Histogram statistics for image enhancement Let r denote a discrete
Histogram statistics for image enhancement Let r denote a discrete

... products of the filter coefficient and the pixels encompassed by filters. For a mask of m x n, we assume that m= 2n+1 and n=2b+1 where a, b a position integers. In general, linear spatial filtering of an image of size M x N with filter size m x n is given by g (x, y)=∑ ...
+ X(t)
+ X(t)

... Example 1 • Consider a CT-LTI system. Assume the impulse response of the system is h(t)=e^(-at) for all a>0 and t>0 and input x(t)=u(t). Find the output. y (t )  h(t )  x(t )  h(t )  u (t ) ...
EEE 302 Lecture 15
EEE 302 Lecture 15

1

Convolution



In mathematics and, in particular, functional analysis, convolution is a mathematical operation on two functions f and g, producing a third function that is typically viewed as a modified version of one of the original functions, giving the area overlap between the two functions as a function of the amount that one of the original functions is translated. Convolution is similar to cross-correlation. It has applications that include probability, statistics, computer vision, natural language processing, image and signal processing, electrical engineering, and differential equations.The convolution can be defined for functions on groups other than Euclidean space. For example, periodic functions, such as the discrete-time Fourier transform, can be defined on a circle and convolved by periodic convolution. (See row 10 at DTFT#Properties.) And discrete convolution can be defined for functions on the set of integers. Generalizations of convolution have applications in the field of numerical analysis and numerical linear algebra, and in the design and implementation of finite impulse response filters in signal processing.Computing the inverse of the convolution operation is known as deconvolution.
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