Does Discrete Wavelet Consider Sampling Frequency or Cutoff Frequency of Bandpass Filter? I have EEG signal with a sampling frequency of 128 Hz, and filtered from 1-30 Hz using a bandpass filter. Now I want to know while decomposing the signal; does DWT decomposes it based on sampling frequency or cutoff frequency? Detailed Coefficients one should be 7.5-30 (if consider cutoff frequency), or 32-64 (if consider sampling frequency).
If we consider the cutoff frequency, we now that upper limit is a bit higher than 30, so how can we correctly justify it?
I am using python pywavelets and want to compute the frequency range of decomposed level.
THe DWT does not really know about the actual sampling. It do cares about the relative frequency span. And it has not knowledge about pre-processing, like linear filtering.
So in your case, the detail coefficients of the first level of wavelet coefficients correspond,  more or less, to the [128/2-128]/2 frequency range.
Because of the initial [0-30] low-pass filter, the above [32-64] first wavelet subband range is likely to contain little useful information.