In general the process of deconvolution can be thought of as an inverse problem in which we wish to recover some original input signal, from the output signal of a system where we have a model of how the input is transformed into the output
The MATLAB decconv function is useful for linear discrete time filtering problems (Please see details below) It sounds like you are trying to perform some other type of inverse problem, which can not be handled using deconv. If you further describe exactly what problem you are trying solve what is your input signal, how is it transformed to an output and how do you propose to "invert" this process then you may be able to get further suggestion for how to proceed.
The MATLAB deconv function (I think this is what you are referring to by "deconvolute") simply does polynomial long division. It can be applied in the above sense to solve an inverse problem in the case of FIR (finite impulse response) discrete time filters. The response of the FIR filter to a finite length input signal can be found in the time domain by convolving the signal with the FIR filter's impulse response. Equivalently we can find the z-transforms of the input signal and the filter impulse response. These are both polynomials in z. Since multiplication in the z-domain is equivalent to convolution in the time domain the filter response, in the z domain can be found by multiplying the inputs signal's z transform polynomial representation and the filter's z-transform polynomial representation. The inverse, deconvolution, problem can then be solved by dividing the z-transform polynomial representation of the output by the z-transform of the filters impulse response. Thus we use MATLAB's deconv function to perform the necessary polynomial long division.
