6
0 0 0 1 1+2xS S Smear Anti-smear unknown ampl. Q P 0 = P x 0 + Q x S + P x 1 P = -Q x S 1+2xS = 2 x P x S + Q x 1 Q = (1 + 2 x S) / (1 – in matlab : Q = (1 + 2*S) / (1 – 2 * S^2) ; R = Q * [-S 1 -S] ; uD = conv(D,R) ; 3 point anti-smear convolution filter D uD input output ‘un-smeared’ results

0 0 0 1 1+2xS S Smear Anti-smear unknown ampl. Q P 0 = P x 0 + Q x S + P x 1 P = -Q x S 1+2xS = 2 x P x S + Q x 1 Q = (1 + 2 x S) / (1 – 2 x S 2 ) in matlab

Embed Size (px)

Citation preview

Page 1: 0 0 0 1 1+2xS S Smear Anti-smear unknown ampl. Q P 0 = P x 0 + Q x S + P x 1 P = -Q x S 1+2xS = 2 x P x S + Q x 1 Q = (1 + 2 x S) / (1 – 2 x S 2 ) in matlab

0

0

0

1

1+2xS

S

Smear

Anti-smear

unknown ampl.

Q

P

0 = P x 0 + Q x S + P x 1 P = -Q x S

1+2xS = 2 x P x S + Q x 1 Q = (1 + 2 x S) / (1 – 2 x S2)

in matlab : Q = (1 + 2*S) / (1 – 2 * S^2) ;

R = Q * [-S 1 -S] ;

uD = conv(D,R) ;

3 point anti-smearconvolution filter

D

uD

input

output

‘un-smeared’ results

Page 2: 0 0 0 1 1+2xS S Smear Anti-smear unknown ampl. Q P 0 = P x 0 + Q x S + P x 1 P = -Q x S 1+2xS = 2 x P x S + Q x 1 Q = (1 + 2 x S) / (1 – 2 x S 2 ) in matlab

a Compensation Filtercourtesy of G.Rehm DLS

FFT

IFFT

Inversethese coeff. at 0 in my first simpleanti-smear,Kees

Page 3: 0 0 0 1 1+2xS S Smear Anti-smear unknown ampl. Q P 0 = P x 0 + Q x S + P x 1 P = -Q x S 1+2xS = 2 x P x S + Q x 1 Q = (1 + 2 x S) / (1 – 2 x S 2 ) in matlab

In blue : ‘3’ point anti-smear filter

In green : ‘5’ point anti-smear filter

Page 4: 0 0 0 1 1+2xS S Smear Anti-smear unknown ampl. Q P 0 = P x 0 + Q x S + P x 1 P = -Q x S 1+2xS = 2 x P x S + Q x 1 Q = (1 + 2 x S) / (1 – 2 x S 2 ) in matlab
Page 5: 0 0 0 1 1+2xS S Smear Anti-smear unknown ampl. Q P 0 = P x 0 + Q x S + P x 1 P = -Q x S 1+2xS = 2 x P x S + Q x 1 Q = (1 + 2 x S) / (1 – 2 x S 2 ) in matlab

ZOOM of previous slide

Page 6: 0 0 0 1 1+2xS S Smear Anti-smear unknown ampl. Q P 0 = P x 0 + Q x S + P x 1 P = -Q x S 1+2xS = 2 x P x S + Q x 1 Q = (1 + 2 x S) / (1 – 2 x S 2 ) in matlab

maf

Standardraw data

5-pointAnti-smear3-point

Anti-smear

Note : horizontal shifts between 4 curves are deliberateto better distinguish the curves