NMR signal averaging — why sum many FIDs? In Fourier-transform NMR, why is it advantageous to acquire many free induction decays (FIDs) from the same sample and add them together before Fourier transforming?

Introduction / Context:
FT-NMR relies on measuring weak time-domain signals (FIDs) that decay due to relaxation. Random electronic and thermal noise is uncorrelated from scan to scan, whereas the true NMR signal is coherent. Repeating the experiment and averaging the results is a universal strategy to enhance sensitivity without changing sample concentration or magnet strength.

Given Data / Assumptions:

• Noisy FIDs contain both coherent signal and random noise.
• Successive scans are performed under identical conditions with adequate relaxation delays.
• Signal averaging follows root-N improvement for random noise.

Concept / Approach:

When N scans are summed, the coherent signal adds linearly (proportional to N), while uncorrelated noise adds as the square root of N. Therefore, the signal-to-noise ratio (SNR) improves approximately by sqrt(N), enabling detection of weak resonances and better quantitative integration. This is fundamental to multidimensional NMR and trace analyte detection.

Step-by-Step Solution:

Verification / Alternative check:

Plotting SNR versus number of scans reveals near sqrt(N) dependence until systematic noise or drift dominates. This empirical behavior underpins standard NMR acquisition parameters (NS).

Why Other Options Are Wrong:

Not every nucleus must be excited individually (A); RF pulses excite ensembles. Field fluctuations (B) are managed by shimming and lock systems; averaging does not primarily fix B0 drift. T1 (E) is an intrinsic property and is not altered by averaging.

Common Pitfalls:

Using too short a recycle delay so spins do not fully relax, causing saturation and non-linear signal growth; ignoring drift that can limit averaging benefits.

Final Answer:

To increase sensitivity by improving the signal-to-noise ratio through signal averaging