@Article{CiCP-15-5,
author = {},
title = {A Frequency Determination Method for Digitized NMR Signals},
journal = {Communications in Computational Physics},
year = {2014},
volume = {15},
number = {5},
pages = {1343--1351},
abstract = {<p style="text-align: justify;">We present a high precision frequency determination method for digitized
NMR FID signals. The method employs high precision numerical integration rather
than simple summation as in many other techniques. With no independent knowledge of the other parameters of a NMR FID signal (phase $ϕ$, amplitude $A$, and transverse relaxation time $T_2$) this method can determine the signal frequency $f_0$ with a
precision of 1/(<span style="text-align: justify;">8$π^2$$f^2_0$$T^2_2$</span><span style="text-align: justify;"></span>) if the observation time $T$ ≫&nbsp;$T_2$. The method is especially
convenient when the detailed shape of the observed FT NMR spectrum is not well
defined. When $T_2$ is +∞ and the signal becomes pure sinusoidal, the precision of the
method is 3/(2$π^2$$f^2_0$$T_2$) which is one order more precise than the ±1 count error induced precision of a typical frequency counter. Analysis of this method shows that the
integration reduces the noise by bandwidth narrowing as in a lock-in amplifier, and
no extra signal filters are needed. For a pure sinusoidal signal we find from numerical
simulations that the noise-induced error in this method reaches the Cramer-Rao Lower
Band (CRLB) on frequency determination. For the damped sinusoidal case of most interest, the noise-induced error is found to be within a factor of 2 of CRLB when the
measurement time $T$ is 2 or 3 times larger than $T_2$. We discuss possible improvements
for the precision of this method.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.110613.270913a},
url = {https://global-sci.com/article/80537/a-frequency-determination-method-for-digitized-nmr-signals}
}