I have a discrete signal of random length (let's say between 500 and 800 in time). This signal has an important information which I want to collect and to put it together in a feature vector to train a classifier. The signal also comes in random phase and in random scale (it depends on the distance to the sensor).
So there are some constraints: the feature vector has to be invariant to scale and phase, it has to be a sparse representation of the information contained in the signal and it has to deal with the problem of different signal length.
I have followed a classic approach to solve this problem:
I calculate the Fourier coefficients of the signal, a[n] and b[n]. I take as feature vectors the most significant coefficients for my problem (I fix this parameter experimentally). To solve the problem of scale and phase invariance I consider only the normalized magnitude r[n] = s[n]/s where s[n] = sqrt(a[n]^2+b[n]^2).
This solution actually works quite well, but I am sure that there has to be something more "up-to-date" to solve that. I would really appreciate any alternative approaches to solve this problem or some references to read.