Multiplets

Author

Sam Hutchins

Published

March 8, 2025

Possible Application of NMR multiplets to Radio Frequency Display.

I stumbled across a new (to me) library mentioned in an article in R-bloggers where Bryan Hanson () had developed a () function to draw complex multiplets, a splitting tree and annotations, inspired by Roman A. Valiulin’s book NMR Multiplet Interpretation.

First, some eye candy:

Code 
library(SpecHelpers) 
peaks1 <- data.frame(
delta = c(4.20, 3.34, 2.23, 1.88, 1.28, 0.94),
mult = c(4, 3, 1, 5, 3, 3),
J = c(14, 14, 0, 14, 14, 14),
area = c(2, 1, 3, 2, 3, 3),
pw = c(2, 2, 2, 2, 2, 2))
# A, B, C, D, E, F
AM <- matrix(c(0, 0, 0, 0, 1, 0, # A
0, 0, 0, 1, 0, 0, # B
0, 0, 0, 0, 0, 0, # C
0, 1, 0, 0, 0, 1, # D
1, 0, 0, 0, 0, 0, # E
0, 0, 0, 1, 0, 0), # F
ncol = 6)
### 1D 1H NMR plot for reference
# CRAN checks will skip some examples to save time
jnk <- plotNMRspec(peaks = peaks1, x.range = c(0, 5), MHz = 500,
main = "1H NMR of ethyl 2-ethyl-3-oxobutyrate")

Just for reference, the above image depicting the NMR spectrum of Butanoic acid, ethyl 2-ethyl-3-oxobutyrate has many uses, such as flavoring for example. This example, plotted at 500 MHz, is found in SpecHelpers package of the CRAN repository.

But, that’s not the purpose of this post. As I was trying some of the examples shown in the above-referenced posting, I noticed the similarity to Amplitude/Frequency Modulated RF signals which when multiplexed to audio/baseband signals, look similar. So I decided to investigate if there were any possible applications for showing AM or FM signals akin to a spectrum analyzer’s display, perhaps for teaching purposes.

We’ll dive in with a sample showing the actual multiplets in all their glory:

Code 
res <- multiplet(J= c(10,10))

That’s very nice if we wished to show the splitting tree, but not really suitable for frequency/modulation depiction, so let’s turn off the plotJtree function. Then we can create a simple single frequency display showing a carrier modulated with a frequency, showing 10:1 ratio.

Code 
res <- multiplet(J= c(10,10), plotJtree=F)

If we wanted a somewhat noisy FM signal with modulation, we might see this:

Code 
res <- multiplet(J = c(15, 10.1, 7.7, 6.7, 3.2, 4.2), plotJtree=F)

There are many methods to create signals of various frequencies with various levels of modulation. I am still exploring additional ways to create more specific signals. It is a work in progress, so there may be more sequels to this post.

But for now, other things call. God Bless and hopefully you have accepted Jesus as your Lord and Savior. Don’t wait too long…

References

Hanson, Bryan. 2025. “A Function to Draw Complex Multiplets.” March 6, 2025. https://chemospec.org/posts/2025-03-06 More Multiplets/MoreMultiplets.html.
R Core Team. 2024. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. https://www.R-project.org/.

Footnotes

  1. Nuclear Magnetic Resonance spectroscopy is one of the most important methods to identify molecular structures, particularly of organic compounds.↩︎

  2. Molecular Formula: C8H14O3↩︎

  3. Amplitude modulation is a technique used in electronic communication where the amplitude of a carrier wave is varied in proportion to the message signal.↩︎

  4. Frequency modulation is the encoding of information in a carrier wave by varying the instantaneous frequency of the wave.↩︎