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## Math Meth Sig Proc

by: Ophelia Ritchie

37

0

1

# Math Meth Sig Proc EECS 551

Ophelia Ritchie
UM
GPA 3.8

Staff

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COURSE
PROF.
Staff
TYPE
Class Notes
PAGES
1
WORDS
KARMA
25 ?

## Popular in Engineering Computer Science

This 1 page Class Notes was uploaded by Ophelia Ritchie on Thursday October 29, 2015. The Class Notes belongs to EECS 551 at University of Michigan taught by Staff in Fall. Since its upload, it has received 37 views. For similar materials see /class/231542/eecs-551-university-of-michigan in Engineering Computer Science at University of Michigan.

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Date Created: 10/29/15
SPLINES AND BATTLELEMARIE WAVELET Splines Piecewise polynomial approximation to functions 1 Divide up real line into intervals 2 Within interval use polynomial of degree k 3 At boundaries called knots have continuous Lia 11 Basis for spline spaces B splines B s VampK notation is awful Summary of notation source B s 7quotB s fsampledB s VampK sWNw sm w BWNM aey SNW SNltW SNltW De nitions sinw2 2N B spllne order 2N 1 SQN1ltCU W2 2N1 B spline order 2N SQNltCUgt e JI V2 Note even order splines shifted by 12 in time so that snt7 0for0lttltN1 80tpulse 31ttriangle 82tquadratic etc VkN piecewise polynomials of degree N over intervals 2 2kj 1 j E integers having continuous 12 at t ij Have chain of subspaces V1N C VON C V C gt sNt satis es 2 scale equation Mt Orthogonal to its integer translations f H f lttt jdtsampled autocorrelation 1 1 J 0 d j0 e 22 Xltw 2km 1 sampling induces periodicity in w

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