Signal Operations If we represent finite-length signals as vectors in Euclidean space, many operations on signals can be encoded as a matrix-vector multiplication. Consider for example a circular shift in C3:delay by one (i.e.a right shift) transforms the signal x = [x0 x1 x2]T into x' = [x2 x0 x1]T and it can be described by the matrix [ 0 0 1 ] D = [ 1 0 0 ] [ 0 1 0 ] so that x' = Dx Determine the matrix F that implements the one-step-different operator in C3 i,e, the operator that transforms a signal x into 1/√ 2[(x0 + 0.5x1 - x2 ) (x1 - 2x0 + x2 ) (x2 - x1)]T
Signal Operations If we represent finite-length signals as vectors in Euclidean space, many operations on signals can be encoded as a matrix-vector multiplication. Consider for example a circular shift in C3:delay by one (i.e.a right shift) transforms the signal x = [x0 x1 x2]T into x' = [x2 x0 x1]T and it can be described by the matrix [ 0 0 1 ] D = [ 1 0 0 ] [ 0 1 0 ] so that x' = Dx Determine the matrix F that implements the one-step-different operator in C3 i,e, the operator that transforms a signal x into 1/√ 2[(x0 + 0.5x1 - x2 ) (x1 - 2x0 + x2 ) (x2 - x1)]T
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Signal Operations
If we represent finite-length signals as vectors in Euclidean space, many operations on signals can be encoded as a matrix-vector multiplication. Consider for example a circular shift in C3:delay by one (i.e.a right shift) transforms the signal
x = [x0 x1 x2]T into x' = [x2 x0 x1]T and it can be described by the matrix
[ 0 0 1 ]
D = [ 1 0 0 ]
[ 0 1 0 ]
so that x' = Dx
Determine the matrix F that implements the one-step-different operator in C3 i,e, the operator that transforms a signal x into
1/√ 2[(x0 + 0.5x1 - x2 ) (x1 - 2x0 + x2 ) (x2 - x1)]T
![√2
[(x₁+0.5x₁ - x₂) (x₁ - 2x₁+x₂) (x₂-x1)]¹
2) –](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbbfa34cd-5e73-4082-8c8b-8a10084015b1%2F24668be9-dc93-48d3-8a23-4ca5552ea7d9%2Fy2rp92r_processed.png&w=3840&q=75)
Transcribed Image Text:√2
[(x₁+0.5x₁ - x₂) (x₁ - 2x₁+x₂) (x₂-x1)]¹
2) –
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