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My math is a little bit rusty. I am learning a lot of stuff recently and some stuff is not clear yet. I ask anybody answering this, to not answer using complex mathematical notation because like I said, my math is rusty.

So, forgive me my ignorance.

I have this discrete time series signal and I want to filter it using Discrete Wavelet Decomposition. I am using Daubechies 4 type wavelets.

I have read in a lot of papers that to do that filtering I need to zero some coefficients in the way up, or in other words, in the inverse decomposition.

Let's represent the signal by S.

If I understood it correctly, this is what I have to do for a 4 level decomposition, filtering and reconstruction of the signal:

  1. First I do a DWT on the signal and obtain the low and high frequency values:

    (lowF1, highF1) = decompose(s)

  2. Then I decompose lowF1 and obtain the second level low and high frequency values:

    (lowF2, highF2) = decompose(lowF1)

  3. I repeat the process and decompose lowF2 and obtain the third level low and high frequency values:

    (lowF3, highF3) = decompose(lowF2)

  4. I repeat the process and decompose lowF3 and obtain the fourth level low and high frequency values:

    (lowF4, highF4) = decompose(lowF3)

Now it is time to filter and reconstruct the signal. I understand that I have to replace the high frequency part with an array of zeros, that will be what is called the threshold.

If that is true, to reconstruct the signal I do:

newSignalLevel3 = reconstruct(lowF3, zeroArray)
newSignalLevel2 = reconstruct(newSignalLevel3, zeroArray)
newSignalLevel1 = reconstruct(newSignalLevel2, zeroArray)
newSignal       = reconstruct(newSignalLevel1, zeroArray)

It it the way to do it?

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Thresholding is to throw away only the coefficients which have lower absolute value than some value (the threshold). Depending on programming language this can be done in different ways.

In c or c++ you may want use for-loop:

for(int i=0; i<N_samples_highF1; i++) 
    if (absolute_value(highF1[i]) < thres) 
        highF1[i] = 0;

And then similarly for the other arrays.

Then you can use these highF1, highF2 et.c. in reconstruction instead of the all-zero arrays.

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    $\begingroup$ Let's see if I got it. I have highF1, highF2, highF3 and highF4. Then I zero all values of these 4 arrays below a certain value. Then I use these new high frequencies arrays to reconstruct the signal, right? $\endgroup$ – SpaceDog Mar 19 at 19:08
  • $\begingroup$ Yep it sounds right. $\endgroup$ – mathreadler Mar 19 at 19:28
  • $\begingroup$ brilliant, thanks!!!!!!!!!!!!!!!! $\endgroup$ – SpaceDog Mar 19 at 19:40

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