The type of wavelet defines you the number of elements and vanishing moments for the scaling and wavelet functions, having "N" taps for a 'dbN' wavelet mother function. 

Let's define it by N=4, the 'db4 wavelet. You have an R^8 base and the scaling (for approximation coefficients) and wavelet (for detail coefficient) functions will have 4 elements: h0, h1, h2 and h3 for scaling; g0, g1, g2, g3 for wavelet. 

Let's say that we have an 8 element signal (N=8): s=[s0 s1 s2 , ... , s8]. The calculation of the coefficients comes from the next product of matrices:

[h0 h1 h2 h3 0 0 0 0; g0 g1 g2 g3 0 0 0 0; 0 0 h0 h1 h2 h3 0 0, 0 0 g0 g1 g2 g3 0 0; 0 0 0 0 h0 h1 h2 h3; 0 0 0 0 g0 g1 g2 g3; 0 0 0 0 0 0 h0 h1 h2 h3; 0 0 0 0 0 0 g0 g1 g2 g3] X [s0 s1 s2 s3 s4 s5 s6 s7];

Notice that since we need to calculate the inner products for every combination the final rows have more elements. We need to add the products between s[N] and s[N+1] which are elements that doesn't exist. It doesn't happen in the Haar wavelet ('db2'), where the R^2 matrix and inner products can be completed.  In this case the extra elements are just pasted from the beginning (i.e. s[N]= s[0] and s[N+1] = s[1]), treating the signal as "periodic". You can just drop out this elements in order to complete the calculation like in 'db2'. You will have the same case in a 'dbN' wavelet. 

I took the information from this website: 

http://www.bearcave.com/misl/misl_tech/wavelets/daubechies/index.html

I also recommend you the Gilbert Strang's book "Wavelets and filter banks" where you will find the relations between wavelets and linear algebra. 

Hi Roilhi Ibarra much thanks for your kind respones

If we do convolution of two signals of length N and M then the output will have the length of M+N-1. your input signal is of 1024=M and filter length is described by dbN (where N=2*4 for db4 or N=2*6 for db6). Then just calculate the corresponding length and down sample to get the length of the final signal. Simple :)

Plz go through the detail about the length and level of the filter. I think you may refer the book on Wavelets by Bopardikar.

You should use non redundant wavelet decomposition. you can use stationary wavelet transform (SWT) in matlab, to get same number of coefficients in each decomposition level.

You have a boundary extension problem.

When you perform a wavelet decomposition you need to apply filters to signals. The question is how the filtering is implemented, and particularly when using finite length signals, what hypothesis are applied to the signals.

Suppose you have a length N signal x[n], with n from 0 to N-1. Suppose that you implement the filtering with a usual linear convolution. The usual hypothesis in that case is that outside the interval of length N where you have known values, the signal is zero. So if you apply a filter of length M to a signal of length N by linear convolution, you get N+M-1 coefficients.

The problem of this approach is that, if you signal begins or ends with values that are far from zero, as you suppose the next sample to be zero you introduce a large discontinuity which will be reflected in the wavelet coefficients as large values at the boundaries, which are artifacts.

Now suppose that you apply a different hypothesis, assuming that you have a period of length N of a periodic signals. That is, outside the known N values, they repeat themselves again and again. Under that hypothesis, the filtering should be implemented as a circular convolution, also known as periodic convolution. In that case the result will have length N, and the resulting wavelet transform will have the same number of coefficients than the original signal.

As with te zero padding case, if your signal begin and ends with values that are far from each other, the prioritization will introduce a large discontinuity at the edges, again generating artifacts.

This is called the signal extension method. In matlab, this can be selected by the command dwtmode. For example, if you use dwtmode('zpd') you will use the first case, and if you ser dwtmode('per') you will set the second.

There are also other methods of signal extension. One is folding, where you "mirror" your signal at the edges, thus avoiding jump discontinuities. This can be selected by dwtmode('sym'). Nevertheless, this will introduce a discontinuity in the derivative of the signal at the edges. To avoid this you can use an antisymmetric padding, which is mirroring with sign change (set by dwtmode('asym') ). Each extension mode has its advantages and disadvantages. The most used one is periodization, as it produces a faster code (it needs less operations) and also it is the only one that produce exactly the same number of resulting coefficients as the length of the original signal.

Here is another way

Set the DWT mode to 'per'. Then the wavedec and waverec functions will use periodic extension of signals for computing the DWT coefficients and reconstructing the signal. The number of coefficients will be same as size of siganl.

dwmode('per')

[c, l] = wavedec(x, 3, 'db4')

x_rec = waverec(c, l, 'db4')

For an example, see https://sparse-plex.readthedocs.io/en/latest/book/wavelets/wavelet_toolbox/daubechies.html#decomposition-with-periodic-extension

From Wavelet toolbox user's guide (Matlab)

"..actual lengths of the detail and approximation coefficient vectors are slightly more than half the length of the original signal. This has to do with the filtering process, which is implemented by convolving the signal with a filter. The convolution “smears” the signal, introducing several extra samples into the result.

How to perform multilevel wavelet reconstruction using coefficients matrices not wavelet decomposition structure [C,S]?