Overview of the problem:
I have a quite complicated filtering application here that I could really use some help and insight on. I'm trying to extract a repetitive signal (a pulse) that is not cyclical but appears on certain modulus. (Meaning a pulse could come 2 to 5 modulus after another.) This places the signal in a certain band, we'll call it the I band, as in the signal of interest. Now there's a bit of background noise, repetitive, cyclical, but varies in phase and frequency slightly over time. (This is caused by a mechanical device!) The device creates one signal with a very strong amplitude, that has it's principle energy in about 4 different bands. The first is slightly lower than I, the next is I itself, and the next two are slightly higher than I. We'll call these principle frequencies A,B,C, with I appearing after A and before B in order of increasing frequency from left to right. Now while A,B, and C are particular and fairly constant to this device, that is certainly not true of similar devices that will be encountered in the future, so any method of filtering must be adaptive. My goal is to eliminate A,B,C (if need be) and subtract that portion of signal that is caused by any other signal except for the signal of interest in the band I. The presence of the second signal overall gives me a signal to noise ration of about -12dB.
What I've tried so far:
Traditional linear filters, even if they're adaptive, appear to be totally out of the question. Their attenuation of the band I, also results in the attenuation of I itself.
I can quite easily lock on to the cycle of I, create an average of it's cycles, and subtract an approximate guess from the current cycle. This produces mixed results.
I've tried using independent component analysis, but this technique seems to rely on the fact that the two signals are in separate bands.
Using a short time fourier transform, I can generally see the change in the I band due to my signal. I have also achieved similar results with the continuous wavelet transform.
Where am at now:
At this point I could really use some community input as to how to handle this. I'd love to hear if anyone has had the same problem, has any suggestions, knows of any literature that could help me, or anything at all.
Thank you very much for your time.
Regards,
Ken
