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<math>x(n_1,n_2)**h(n_1,n_2)=\bigg(\sum_{k_1=-\infty}^{\infty} h(k_1)x(n_1-k_1)\bigg)\bigg(\sum_{k_2=-\infty}^{\infty}h(k_1)x(n_1-k_1)\bigg)</math>
It is readily seen then that this reduces to the product of
<math>x(n_1,n_2)**h(n_1,n_2)=\bigg[x(n_1)*h(n_1)\bigg]\bigg[x(n_2)*h(n_2)\bigg]</math>
This conclusion can then be extended to the convolution of two separable ''M''-dimensional signals as follows:
<math>x(n_1,n_2,...,n_M)*...*h(n_1,n_2,...,n_M)=\bigg[x(n_1)*h(n_2)\bigg]\bigg[x(n_2)*h(n_2)\bigg]...\bigg[x(n_M)*h(n_M)\bigg]</math>
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