Signal processing in spectroscopy – How do you convert a time-domain NMR signal (free induction decay) into a frequency-domain spectrum?

Introduction / Context:
Modern NMR and many spectroscopies rely on pulsed excitation and detection in the time domain. The recorded free induction decay (FID) contains all the spectral information, encoded as exponentially decaying sinusoids. To interpret chemical shifts and coupling patterns, we must convert this time-domain signal into a frequency-domain spectrum using the Fourier transform (FT). This is the basis of FT-NMR.

Given Data / Assumptions:

• After an RF pulse, nuclear magnetization precesses and decays, producing the FID.
• Sampling is uniform, and digitization obeys the Nyquist criterion for the spectral width.
• Spectral processing may include apodization and zero-filling to improve appearance.

Concept / Approach:
The Fourier transform decomposes the FID into constituent frequencies, revealing resonance positions (chemical shifts) and line shapes. Phase correction aligns absorptive and dispersive components. Apodization (windowing) trades resolution for signal-to-noise in a controlled way, and zero-filling increases digital resolution without adding information.

Step-by-Step Solution:

Verification / Alternative check:
Compare spectra processed with and without the FT step: only after FT do distinct peaks at specific frequencies (ppm) appear, confirming that Fourier transformation is essential.

Why Other Options Are Wrong:

• Peak-area measurement is an analysis step, not a transformation.
• Michelson interferometers are used in FT-IR optics; the mathematical conversion is still a Fourier transform, and NMR does not use a Michelson interferometer.
• Wavelet averaging or “none” cannot replace FT for standard NMR spectra.

Common Pitfalls:
Confusing hardware used in other spectroscopies with the mathematical transformation required; in NMR, FT is the universal route from time to frequency domain.

Final Answer:
Fourier transformation