Dual propagation inversion of truncated signals

Fourier transforms occur in a variety of chemical systems and processes. A few examples include obtaining spectral information from correlation functi ons, energy relaxation processes, spectral densities obtained from force au tocorrelation functions, etc. In this article, a new functional transform, named the dual propagation inversion (DPI) is introduced. The DPI Functiona l transform can be applied to a variety of problems in chemistry. such as F ourier transforms of time correlation functions. energy relaxation processe s, rate theory. etc, The present illustrative application is to generating the frequency representation of a discrete, truncated time-domain signal. T he DPI result is compared with the traditional Fourier transform applied to the same truncated time signal. For both noise-free and noise-corrupted ti me-truncated signals, the DPI spectrum is found to be more accurate. partic ularly as the signal is more severely truncated. In the DPI, the distribute d-approximating-functional free propagator is used to propagate and denoise the signal simultaneously.