Signal Processing / Deconvolution Question-

Hi-

I have an arbitrary sample 1D waveform that I am trying to deconvolve into a series of 5 known component 1D waveforms. Adding the component waveforms with an arbitrary integer coefficient in front of each should produce the sample waveform (approximately).

Currently I am using a gradient minima finder (fminunc) to iteratively add the component waveforms together using various integer coefficients in front of each waveform. I minimize the difference between the sample and the 'summed' waveform, and report back the integer coefficients for each component waveform that minimizes this difference.

I believe this can be done with deconvolution, however when I send in a sample waveform and one of the component waveforms, I receive out a single very low number for my q value and a remainder of approximately the entire sample waveform. I also know that my component waveforms were not 'scanned' across the space in x to create the sample waveform (as is the case in convolution). In other words, the component waveform contribution will only occur when it is aligned with the first sample at x=0. Perhaps deconvolution isn't the technique I want.

Simply doing a matrix divide between the sample waveform and each component waveform doesn't account for the fact that there is overlap in the component waveforms. I want to find the optimal parameters that adds all component waveforms to obtain the sample waveform. Assuring I don't get caught in a local minimum is a priority.

Can anyone offer some advice or point me towards some reading material to up my knowledge on how to tackle this problem? Thanks in advance!

-Ryan