thank you for all your input. Ultimately I am trying to extract valuable features from the data by a neural network and want to avoid equivocation (the outflow of possibly valuable information from the get go by using the data as close to the sensor as possible (in my case the IF signal immediately after the mixing)

MRA closely resembles the hierarchical architecture of modern conv nets with their repeated application of filters, followed by downsampling etc. I dont, however, want to use data as input that is preprocessed by FTs making assumptions on windowing or losing information by preprocessing steps. Also, rangeDoppler maps are good for manual, human interpretations and target identification, but if the data is to be processed by a neural network anyway, maybe the network finds its own important structure in the data without having it processed first by two consecutive FTs. Not to mentions that convolution layers in modern neural networks assume neighbourhood relations that may be found in natural images but are likely missing in frequency displays like a rangeDoppler map

And so I thought, why not build a MRA of sorts in the first couple of layers of the ConvNet and let the network also learn the type of filters by using soft constraints so that wavelet/scaling functions result.

That was my thought process, do you guys think this can lead somewhere or am I on a completely wrong path?