Fourier Transform: Difference between revisions
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Fourier Transform does mathematically what our ears do physically: resolve a signal into component frequencies. | Fourier Transform does mathematically what our ears do physically: resolve a signal into component frequencies. FT is a method to determine the simple wave components of a mixed wave. The method is theoretically based on calculus, but is actually carried out computationally using numerical analysis. | ||
The signal output from an NMR instrument is called a Free Induction Decay (FID) and looks like the image on the left, which is intensity of the signal versus time. A fourier transform algorithm is applied to the signal which converts it to intensity versus frequency and looks like the image on the right: | |||
[[File:ethanol_fid_and_spectrum_modified.jpg|500px]] | |||
A good way to see the method in action is to use excel and a simple dataset of times and intensities. A description of how to use excel to do FT is given [https://courses.physics.illinois.edu/phys401/sp2012/Files/Freq%20Analysis/The_Excel_FFT_Function_v1.2.pdf here], but I will summarize it in case this link disappears: | |||
Latest revision as of 19:14, 5 July 2026
Fourier Transform does mathematically what our ears do physically: resolve a signal into component frequencies. FT is a method to determine the simple wave components of a mixed wave. The method is theoretically based on calculus, but is actually carried out computationally using numerical analysis.
The signal output from an NMR instrument is called a Free Induction Decay (FID) and looks like the image on the left, which is intensity of the signal versus time. A fourier transform algorithm is applied to the signal which converts it to intensity versus frequency and looks like the image on the right:
A good way to see the method in action is to use excel and a simple dataset of times and intensities. A description of how to use excel to do FT is given here, but I will summarize it in case this link disappears: