A unified treatment of recursive digital filtering
S. Haykin · IEEE Transactions on Automatic Control · 1972
Using the convolution integral, an integro-difference equation is derived for defining the input-output relation of a linear time-invariant filter. This equation is, in turn, used to obtain the various analog-to-digital filter transformations for the digitization of a continuous transfer function, with each transformation corresponding to a specific way of approximating the continuous time excitation.