Title

A Closed-Form Solution for the Optimal Time Evolution of an Exponentially Decaying Signal with Thermal Noise

Publication Date

2014

Journal

Concepts in Magnetic Resonance Part A

Volume

43

Issue

2

First Page

54

Last Page

56

Abstract

The signal-to-noise ratio of a monoexponentially decaying signal exhibits a maximum at an evolution time of approximately 1.26 T-2. It has previously been thought that there is no closed-form solution to express this maximum. We report in this note that this maximum can be represented in a specific, analytical closed form in terms of the negative real branch of an inverse function known as the Lambert W function. The Lambert function is finding increasing use in the solution of problems in a variety of areas in the physical sciences. (C) 2014 Wiley Periodicals, Inc.

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