# Raw signal to short for DWT

The algorithm i use to apply a discrete wavelet transform only accept raw-data with a certain number of samples (2,4,8,..128..).

I have to either interpolate the raw signal or padding it with zeros (or discard samples if size is e.g 129).

Interpolation would change the samle-rate of the entire data. Therefore I assume that zero-padding would have less effect on the "nature" of the raw signal.

How would zero-padding influence the "nature" of a raw-signal in respect to the DWT?

## 1 Answer

If you're talking about affecting the Perfect Reconstruction (PR) properties of a wavelet transform using wavelets with the PR property, then it won't affect it at all. I.e., you can transform the zero-padded signal, then apply the inverse transform to the result, and you will get the original (zero-padded) signal again. Remove the zeros from the reconstructed signal and you have the (actual) original signal.

As far as the DWT is concerned, the zero-padded signal IS the original signal. So if you keep track of how many zeros you added before the decomposition, then you can just remove the same number after reconstruction.

Of course, modifying any of the coefficients before reconstruction will introduce artifacts into the result, but this isn't related to the fact that you zero-padded the input signal. However, it can result in aliasing effects in the area which should otherwise be all zeros (after reconstruction). But if, after reconstruction, you simply remove those values which weren't part of the "original signal" (the signal before you zero-padded it), then it won't make any difference (there could still be aliasing effects in the rest of the signal if you change the coefficients before reconstruction).

So if you're using zero-padding for the input signal, it doesn't affect the "nature" of the signal at all - it just means that, as far as the DWT is concerned, your original signal is the zero-padded signal and not your actual original signal. Keep track of how many and where (beginning or end) your zeros are and you can just remove those values after reconstruction.