Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question
100%

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) –
Transcribed Image Text:√2 [(x₁+0.5x₁ - x₂) (x₁ - 2x₁+x₂) (x₂-x1)]¹ 2) –
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS