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Summary Of: Convolution

is the convolution of functions f and g... is the convolution of functions f and g... Convolution is similar to... The convolution can be defined for functions on... and the discrete convolution can be defined for functions on the set of... These generalizations of the convolution have applications in the field of... the convolution formula can be described as a weighted average of the function... then their convolution may be defined as the integral... coefficients of the product are given by the convolution of the original coefficient... circular convolutions so that fast transforms with a convolution property can be used to implement the computation... convolution of digit sequences is the kernel operation in... and other applications typically use fast convolution algorithms to reduce the cost of the convolution to O... The convolution of two complex... Conditions for the existence of the convolution may be tricky... An important feature of the convolution is that if... Combined with the fact that convolution commutes with differentiation... it is possible to define the convolution of a function with a... is possible to extend the definition of the convolution in a unique way so that the associative law... The convolution defines a product on the... since most collections of functions on which the convolution is performed can be convolved with a delta distribution or... A particular consequence of this is that the convolution can be viewed as a... The convolution commutes with translations... convolution is the most general translation invariant operation... is given as convolution with a function... Each convolution is a compact... can be viewed as a version of the convolution theorem discussed above... and its density function is just the convolution of the two separate density functions... Convolution and related operations are found in many applications of engineering and mathematics... the convolution of one function... is the convolution of their individual distributions... focus photograph is the convolution of the sharp image with the shape of the iris diaphragm... an echo is the convolution of the original sound with a function representing the various objects that are reflecting it... convolution is used to map the... is the convolution of the input... a convolution operation makes an appearance... Visual convolution Java Applet for Discrete Time functions... Convolution Kernel Mask Operation Interactive tutorial...

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convolution (computer science) |

Visual explanation of convolution. 1.Express each function in terms of a dummy variable τ. 2.Transpose one of the functions: g(τ)→g( − τ). 3.Add a time-offset, t, which allows g(t − τ) to slide along the τ-axis. 4.Start t at -∞ and slide it all the way to +∞. Wherever the two functions intersect, find the integral of their product. In other words, compute a sliding, weighted-average of function f(τ), where the weighting function is g( − τ). The resulting waveform (not shown here) is the convolution of functions f and g. If f(t) is a unit impulse, the result of this process is simply g(t), which is therefore called the impulse response.

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Convolution".