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Math · Advanced Math
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In C^N any linear operator on vector x can be expressed as a matrix-vector multiplication for a suitable matrix A. Define the delay operator as the right circular shift of a vector: D{x} = [xN-1n0x1...xN-2].

Assume N = 4 for convenience; it is easy to say that D{x} = [0 0 0 1, 1 0 0 0, 0 1 0 0, 0 0 1 0] where the delay operator D is indicated as D{x[n]} = x[n-1]

Using this definition of the differentiation operator x[n] - x[n-1] write out the matrix form of the differentiation operator in C^4.

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