Reconstruct the signal using wavelet

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

Answer 1

[Wayne King]

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.

[Fuad Numan]

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

Answer 2

[Wayne King]

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);

[Fuad Numan]

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]);

[Alaa Gouda]

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 ???