Further Examples: ListConvolve

This gives the convolution of with .

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Matrices such as this one can be used to illustrate how convolutions work. The elements of the convolution are formed by taking the dot product of the first row with each of the other rows. Spaces are used instead of zeros for clarity.

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In this case the element x at position of the kernel is aligned with each element of the list in turn.

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Here the element y at position of the kernel is aligned with each element of the list.

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This forms the cyclic convolution whose first element contains 2 x and whose last element contains 6 x.

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Here the list is padded with repetitions of p.

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This pads the list with p, q. The reversed list is put on top of a cyclic repetition of p, q.

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Here Plus and Times are replaced by Times and Power.

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This multiplies x and y together in base b.

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For instance, this multiplies and in base .

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