Why do we assume the matrix of impulse responses to be a Toeplitz matrix during deconvolution
For any one still interested: I personally think it is because of the assumption that the system is causal + time invariant; output is only dependent on past inputs. Therefore you can see that that its lower triangular. The toeplitz structure is because of the fact the system is assumed to be time invariant. If you think about what causality and time invariance means then you can imagine this structure.