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