## 4 Applications of the Transient Regime
### Fast and Simultaneous T\({}_{1}\) and T\({}_{2}\) Measurements
When the oscillation ends, the signal was named a quasi-stationary state (QSS) (transition between dark and light gray regions). The background color indicates the first transient oscillating signal (dark grey), the slowly signal decay with time constant T* (light grey), given by Equation (5), until it reaches the constant steady state amplitude \(\mid\)M\({}_{\rm ss}\mid\) (white region). \(>>\) T\({}_{2}\) signals were acquired using CuSO\({}_{4}\) (T\({}_{1}\)\(\approx\) j T\({}_{2}\)), and MnSO\({}_{4}\) solution (T\({}_{1}\) = 4T\({}_{2}\)), in a 20 MHz spectrometer. The DR for CWFP is the greatest for T\({}_{1}\)\(>>\) T\({}_{2}\) and narrowest for T\({}_{1}\) = T\({}_{2}\) (Figure 9A). Conversely, the DR of the CP-CWFP signal is the largest for the sample with T\({}_{1}\) = T\({}_{2}\), and the narrowest for T\({}_{1}\)\(>>\) T\({}_{2}\) (Figure 9B). The dependence of DR of T* as a function of the relaxation times ratio was solved using the CP-CWFP with phase alternation, CP-CWFPx-x [24]. Figure 9C shows the CP-CWFPx-x signal for the sample with T\({}_{1}\)\(\approx\) T\({}_{2}\) and T\({}_{1}\)\(>>\) T\({}_{2}\). This figure shows that the T* dynamic range is independent of T\({}_{1}\)/T\({}_{2}\) ratio. Furthermore, the CP-CWFPx-x pulse sequence can be performed on resonance and therefore is the best CWFP sequence for measuring both relaxation times in a single experiment. We demonstrated that the CP-CWFPx-x sequence can be used to measure T\({}_{1}\) in a single shot experiment using a low flip angle (5\({}^{\circ}\) to 10\({}^{\circ}\)), even in a spectrometer with a long dead time [23]. Using these small flip angles, the T* is strongly dependent on T\({}_{1}\) (Equation (4)). Figure 10 provides a comparison between the CP-CWFPx-x with low flip angle (CWFP-T\({}_{1}\)) transition time T* signal, obtained with a single shot experiment, and inversion-recovery (IR) data obtained with 32 experiments. Although the SNR of CWFP-T\({}_{1}\) is much lower than obtained with IR, the T\({}_{1}\) values were similar. We demonstrated that several post-acquisition digital filters (low pass, linear and logarithm compression, Savitzky-Golay, and Wavelet filters) can be used to enhance SNR in CWFP-T\({}_{1}\) signals without significant deviation of the T\({}_{1}\) values [39]. Figure 11 shows a SNR enhancement of one order of magnitude on CWFP-T\({}_{1}\) signal using second-order, a 41-points window, and a Savistiky-Golay (SG) filter. Therefore, filtered CWFP-T\({}_{1}\) can be a fast T\({}_{1}\) method, providing an alternative to CPMG for low-field NMR relaxation measurements. Figure 10: Comparison of Inversion recovery (IR) (black points) and Continuous Wave Free Precession-\(T_{1}\) (CWFP-\(T_{1}\)) (grey line) normalized signals of water sample. Adapted from Publication [23], Copyright (2016), with permission from Elsevier. Figure 9: Experimental (**A**) CWFP, (**B**) CP-CWFP, and (**C**) CP-CWFPx-x signal for solution of CuSO\({}_{4}\) 10 mM (T\({}_{1}\) = T\({}_{2}\)) and MnSO\({}_{4}\) 1 mM solution (T\({}_{1}\) \(>>\)T\({}_{2}\)).