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Reconstruct the signal using wavelet

Asked by Fuad Numan on 6 Apr 2012
Latest activity Commented on by Alaa Gouda on 13 Mar 2017
I have a noisy signal , i want to decompose it and reconstruct a specific sub-band frequencies;
[C2,L2]=wavedec(xn,8,'db8');
% approximation coefficients
A1=wrcoef('a',C2,L2,'db8',1);
A2=wrcoef('a',C2,L2,'db8',2);
A3=wrcoef('a',C2,L2,'db8',3);
A4=wrcoef('a',C2,L2,'db8',4);
A5=wrcoef('a',C2,L2,'db8',5);
A6=wrcoef('a',C2,L2,'db8',6);
A7=wrcoef('a',C2,L2,'db8',7);
A8=wrcoef('a',C2,L2,'db8',8);
%detail coefficients
D1=wrcoef('d',C2,L2,'db8',1);
D2=wrcoef('d',C2,L2,'db8',2);
D3=wrcoef('d',C2,L2,'db8',3);
D4=wrcoef('d',C2,L2,'db8',4);
D5=wrcoef('d',C2,L2,'db8',5);
D6=wrcoef('d',C2,L2,'db8',6);
D7=wrcoef('d',C2,L2,'db8',7);
D8=wrcoef('d',C2,L2,'db8',8);
I have used "waverec" function to reconstruct the whole frequencies except the detail 1 (D1), I used
C=[A8;D8;D7;D6;D5;D4;D3;D2];
L=[length(A8);length(D8);length(D7);length(D6);length(D5);length(D4);length(D3);length(D2);length(xn)];
Rec_signal=waverec(C,L,'db8');
The resulted Rec_signal is too much different from the original signal even not close;
Is that a correct reconstruction code, or i have to sum the coefficients together.
I also want to try omitting other coefficients and rebuild the signal till i get what i want.
appreciate your help

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2 Answers

Answer by Wayne King
on 6 Apr 2012
 Accepted Answer

Are you sure you are getting tmp from
tmp = cumsum(L);
That output cannot be a non-integer, please show me your code and give me the length of your input signal.

  1 Comment

Oh, sorry I missed that one.
Now it is ok
tmp(end-2)+1 = 1111
tmp(end-1) = 2117
which confirms the length of D1
Thank you

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Answer by Wayne King
on 6 Apr 2012

You are using the incorrect input to waverec. waverec expects that the input is the wavelet and scaling coefficients. However you are inputting the output of wrcoef, which is not the wavelet and scaling coefficients.
The output of wrcoef are projections onto vector subspaces, they are the same length as the input signal. Just set the d1 coefficients in the output from wavedec to zero to get what you are looing for and input that into waverec.
load noisdopp;
[C,L] = wavedec(noisdopp,8,'db8');
Cnew = C;
tmp = cumsum(L);
Cnew(tmp(end-2)+1:tmp(end-1)) = 0;
Rec_signal=waverec(Cnew,L,'db8');
plot(noisdopp,'k'); hold on;
plot(Rec_signal,'r','linewidth',2);

  2 Comments

Thank you Wayne
This is my first use of wavlet, this definitely solves my problem, but still cant get it. the indices you put to remove the D1 coefficients are floot (not integer).
how could I know in which range of Cnew indices each coefficient located in.
As per your script,
tmp(end-2)+1 = 3.8112
tmp(end-1) = 0.6585
while the length of D1 is 1007, given from
[D1,D2,D3,D4,D5,D6,D7,D8]=detcoef(C2,L2,[1 2 3 4 5 6 7 8]);
would you please can you help me in my code i decompose signal in 5 levels i want to remove A5 ,D1 How can I do it ???

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