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Recovery of absolute gas absorption line shapes from first harmonic residual AM (RAM) signals in tunable diode laser spectroscopy with wavelength modulation (TDLS-WM) offers significant advantages in terms of measurement accuracy (for gas concentration and pressure), freedom from the need for calibration and resilience to errors, or drift in system parameters/scaling factors. However, the signal strength and SNR are compromised somewhat relative to conventional WM spectroscopy (WMS) by the signal dependence on the laser's intensity modulation amplitude rather than on the direct intensity, and by the need to operate at low modulation index, 0.75 in the previously reported study. In part 1 of this two-part publication, we report a more universal approach to the analysis of recovered RAM signals and absolute absorption line shapes. This new approach extends the use of RAM techniques to arbitrary m values up to 2.2. In addition, it provides the basis for a comparison of signal strength between the RAM signals recovered by the phasor decomposition approach and conventional first and second harmonic TDLS-WM signals. The experimental study reported here validates the new model and demonstrates the use of the RAM techniques for accurate recovery of absolute gas absorption line shapes to 2.2 and above. Furthermore, it demonstrates that the RAM signal strengths can be increased significantly by increasing the modulation frequency and defines regimes of operation such that the directly recovered RAM signals are comparable to or even greater than the widely used conventional second harmonic TDLS-WM signal. Finally, a critique of the RAM techniques relative to the conventional approaches is given.