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I've begun going through a book called "An introduction to geophysical exploration" by Phillip Kearey and Michael Brooks and I've come across a problem I can't for the life of me see how they got their answer.

Essentially, given an input function g_{i}(i = 1,2.... m), and a convolution operator f_{j}(j = 1,2 ......n) the convolution output is given by:

y_{k}= [itex]\Sigma[/itex]g_{i}f_{k - i}(k = 1,2 ..... m + n - 1)

with (Sigma sum starting at i = 1 and going up to m).

Their example is with an input of g(2,0,1) and operator of f(4,3,2,1) the output is y(8,6,8,5,2,1).

Not only can I not see how this is obtained, but based on the function if I'm trying to find y_{1}I end up with negative index of f_{j}as I perform f_{k - i}as i increases from 1 to 3 with the largest index being f_{0}(from f_{1 - 1}where k = 1 and i = 1). How can this be correct?

Any help would be appreciated.

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# Convolution output function

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