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Compute the convolution x(t)×v(t) for −[infinity]

User Latkin
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Final answer:

To compute the convolution of x(t) and v(t), represented as x(t) × v(t), the integral of x(a) multiplied by v(t - a) over all possible values of a is used.

Step-by-step explanation:

The convolution of two functions x(t) and v(t), represented as x(t) × v(t), is a mathematical operation that produces a third function. This function represents the amount of overlap between x(t) shifted by t and v(t) as a function of the shifting. To compute the convolution of two functions, you use the integral:

∑ x(a) · v(t - a) da, over all a from -∞ to ∞.

The convolution integral can be interpreted as the area under the curve of x(a) times v(t-a) as a shifts over all possible values. However, in the practical computation of convolution, the limits of integration are often confined to the domain where the two functions are non-zero.

User Lowell
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