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Tunable diode laser spectroscopy is extremely important for gas detection in a wide variety of industrial, safety and environmental monitoring applications. Of particular interest is the development of calibration-free, stand-alone systems and instrumentation which can operate in high-temperature or high-pressure environments (such as in fuel cells, or gas turbine engines) where continuous and simultaneous monitoring of pressure, temperature and concentration of gases may be required. Here, in Part 1 of this two-part paper, we present the full theoretical basis and range of techniques for calibration-free line-shape recovery to allow simultaneous measurements of concentration and pressure/temperature for a wide range of potential applications. Firstly, on the basis of Fourier analysis, we present the general signal components that arise with both intensity and frequency modulation of diode lasers and identify the issues and difficulties associated with accurate line-shape recovery in conventional wavelength modulation spectroscopy (WMS). We then show how line-shape recovery may be effectively performed using first harmonic signals and, by use of a general correction function from Fourier coefficients, we extend the techniques previously reported to include arbitrary large modulation indices, different line-shape profiles and high gas concentration with non-linear absorption. Previous approximate techniques based on Taylor series expansions are included as a special case of the Fourier analysis for low modulation indices. We also show that the signal amplitudes obtained in this way can be comparable to, or even exceed, that of conventional WMS by appropriate choice of the modulation index and frequency.