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Question 5.E.8.9: Prove that a ⊙ b = b ⊙ a for all a, b ∈ C^n —i.e., convoluti......

Prove that a \odot b = b \odot a for all a, b ∈ \mathcal{C}^n—i.e., convolution is a commutative operation.

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Use (5.8.12) to write a \odot b = F^{-1} [(F\hat{a}) × (F\hat{b})] = F^{-1} [(F\hat{b}) × (F\hat{a})] = a \odot b.

F (a \odot b ) = (F\hat{a}) × (F\hat{b})   and  a \odot b = F^{-1} [(F\hat{a}) × (F\hat{b})].            (5.8.12)

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