A transform approach based on a variable initial time (VIT) formulation is developed for discrete-time signals and linear time-varying discrete-time systems or digital filters. The VIT transform is a formal power series in $z^{-1}$, which converts functions given by linear time-varying difference equations into left polynomial fractions with variable coefficients, and with initial conditions incorporated into the framework. It is shown that the transform satisfies a number of properties that are analogous to those of the ordinary $z$-transform, and that it is possible to do scaling of $z^{-i}$ by time functions, which results in left-fraction forms for the transform of a large class of functions including sinusoids with general time-varying amplitudes and frequencies. Using the extended right Euclidean algorithm in a skew polynomial ring with time-varying coefficients, it is shown that a sum of left polynomial fractions can be written as a single fraction, which results in linear time-varying recursions for the inverse transform of the combined fraction. The extraction of a first-order term from a given polynomial fraction is carried out in terms of the evaluation of $z^i$ at time functions. In the application to linear time-varying systems, it is proved that the VIT transform of the system output is equal to the product of the VIT transform of the input and the VIT transform of the unit-pulse response function. For systems given by a time-varying moving average or an autoregressive model, the transform framework is used to determine the steady-state output response resulting from various signal inputs such as the step and cosine functions.

It is proposed that the human soul is a field consisting of a collection of quantum-like fields that interact only with certain fields in the physical universe, and not directly with matter. Fields that interact with the soul field include electromagnetic waves as evidenced by near-death experiences where events that could not have been seen through the eyes of the individual are verified. Since electric fields and electromagnetic fields have the same quanta consisting of photons, electric fields may also interact with the soul field. This could result in the transfer of information on working memory content to the soul through electric fields produced by neural ensembles in the human brain. The soul field may also affect neurons on the molecular level in the brain through interactions with electric fields and the recently proposed mechanism of cytoelectric coupling.

This addendum contains clarifications and a sharpening of some of the results on the VIT transform framework developed in [1]. The focus is on the right-coefficient and left- coefficient forms of the transform, the extraction of a first-order term from a left polynomial fraction, and the application to linear time-varying systems.