When performing the Discrete Wavelet Transform in MATLAB using the command DWT or WAVEDEC, what it the exact time or pseudo-time location of the DWT coefficients?
At each level the time series is decimated by 2, this means that the coefficients should be localized at $2^j \, T_s$, where $T_s$ is the sampling frequency. However, the application of a reconstruction filter of length $M$ makes the coefficient arrays longer. And each level a longer coefficient array is then fed into a new DWT function, which modifies further its length. The arrays are also properly extended at each level, according to a criterion specified by the user using the command DWTMODE.
I see that in some MATLAB examples, just the central part of the array is shown using the command WKEEP, which shows only the central part of the coefficient array. Is this approach sufficiently accurate, meaning that the external coefficients (those that are not showncentral) are really NOT significant?
If I do not discard some coefficients, I clearly see a huge delay if I assign them to $2^j \, T_s$. I believe that the external coefficients are however necessary for the reconstruction.
How many coefficients can be discarded at each level, if they can be?