Inversion of signal operations

In a variety of applications, one is given the response signal which results when a known linear system (operator) is excited by an unknown input signal. From this information, it is then desired to ascertain the input signal which gave rise to the observed response behavior. An efficient operational, as well as an algorithmic, procedure shall be presented for achieving the desired signal inversion operation. Conditions under which this inversion is well-posed mathematically shall be detailed. The development is carried out in a general normed space setting thereby making the results applicable to a variety of signal inversion problems.