hwsolB07 - This operation can be also seen as a circular...

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Sheet1 Page 1 HW 7 Solution _____________ (i) A = [-4 3 0 02/02/01 1 2 2 ] A*[1 0 (ii) (a) B*x = [2 3 that circularly shifts the elements of the vector x. (b) B^2*x = [3 1 the elements of the vector B*x. (c) B^3*x = [1 2 the elements of the vector B^2*x. (d) B^3*x - x = 0 (e) For any vector x = [x_1 x_2 x_3]^T, we can show that B^3x = x and therefore B^3x-x = 0. (iii) FFTSHIFT swaps the top and bottom halves of a n-dimensional column vector. In the case where n is odd, the first entry is included in the top half and is moved to the center of the vector.
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Unformatted text preview: This operation can be also seen as a circular shift downwards by a n/2 positions if n is even and (n-1)/2 positions if n is odd. The matrix C is given by n = 7: 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 n = 8: 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 Sheet1 Page 2 1] = [-4 1 3] 1]. B is a transformation matrix 2]. Multiplying by B circularly shifts 3]. Multiplying by B circularly shifts...
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hwsolB07 - This operation can be also seen as a circular...

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