Simulating the extraction of signal parameters and spectrograms for non-stationary NMR signals

Free induction decay (FID) signals in nuclear magnetic resonance (NMR) spectroscopy are commonly analyzed using the fast Fourier transform (FFT). This simulation study evaluates complementary methods for short or non-stationary FID signals in which linewidth, dephasing, or decay behavior changes during acquisition. Simulated FIDs containing exponentially damped sinusoids, Gaussian-distributed frequencies, and time-dependent broadening were analyzed using FFT, short-time Fourier transform (STFT), wavelet transform, and direct nonlinear time-domain fitting. Simulations of finite collection windows show that point-sampled FIDs can approximate window-integrated signals after amplitude and phase correction when the collection window is sufficiently sharp and reproducible. FFT remains the fastest and most reliable approach for stationary, sufficiently long, high-signal-to-noise signals. Zero filling improves spectral interpolation but does not recover frequency resolution lost through short acquisition. STFT and wavelet methods reveal time-dependent frequency and decay behavior, although with reduced frequency resolution. Direct time-domain fitting can estimate amplitudes, frequencies, phases, and decay constants from very short, relatively simple FID segments, but its reliability depends on model selection, initial estimates, the number of signal components, and avoidance of local minima. These methods therefore serve complementary roles in analyzing stationary and non-stationary NMR signals.