CWT: selection of scales and filtering

Question

I am using CWT to obtain scalograms of ECG signals as the one below:

In my research, most articles contain a pre-processing step before performing CWT (that usually includes signal normalization and digital filtering). The filtering usually consists on a bandpass filter (for example 0.5 Hz - 100 Hz for the ECG).

My question is if I select a range of scales that will produce pseudo frequencies in the y-axis that correspond to the bandpass filter (0.5 - 100 Hz), will the previous filter have any effect in the scalogram at all?

Answer 1

I suppose that with "selecting a range of scales that will produce pseudo frequencies" one assumes a certain type of windowing in the scalogram domain. This could also be called "time-scale masking". I'd suggest literature like Auditory time-frequency masking: Psychoacoustical measures and application to the analysis-synthesis of sound signals, Thibaud Necciari, PhD thesis, 2010.

The combined effect of the frequency spread of the specific wavelet one is using and of the time-scale masking is likely to produce a filtering result different from what you would obtain with a given family of classical FIR or IIR filter. On top of that, the discretization effect of both wavelet dilation and shift parameters may add some more divergences.

In a nutshell, while most admissible wavelets possess a bandpass behavior, they satisfy other constraints that traditional bandpass filters ignore.

However, with a nice tappering in the time-scale domain and a wavelet well-balanced spectral properties, the difference may become not meaningful.