Definition - What does Convolution mean?

Convolution is a mathematical equation of two functions that correspond to well testing and geophysics. One function is a process of linear or invariant filtering, and is represented as f(t) and the other function is time series that is represented as x(t). In the signal processing, one of the two functions is usually a filter acting on the other function.

Petropedia explains Convolution

Convolution is helpful in mathematically representing responses of many physical systems. A good example where convolution is used is in modelling the filtering of seismic energy by various rock layers in the earth. Similarly, deconvolution is used extensively in seismic processing so as to counteract the filtering during convolution.

The mathematical form of convolution is as follows:

Where y(t) is represented as the convolution’s output,

Similarly, during the frequency, convolution is the product of Fourier Transformation of Filter and Time series in this way:

Y(w) = F(w) * X(w)

Where, Y(w) represents Fourier Transformation of output y(t),

F(w) represents Fourier Transformation of filter f(t),

X(w) represents Fourier Transformation of time series x(t)
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