In this paper a method of correcting modulation broadened signals by means of their Fourier transforms is investigated. It is shown that in the absence of saturation this method, which can be applied for arbitrary line shape functions, provides the true line shape as well as any of its derivatives. The same holds if saturation is present, provided that the modulation frequency is small compared with the spin-lattice relaxation rate and the induced transition probability.by the correction procedure, and a theoretical expression of the signal-noise ratio after correction is derived for the detection of the nth harmonic signal. The conditions for maximization of the signal-noise ratio after correction are given. It is shown that the sensitivity increases for decreasing values of the limits between which the Fourier transformations are performed, limited only by an increasing distortion of the signal. For the first derivatives of a Iorentzian and gaussian line shape this distortion is compared with that due to the modulation broadening. The results are compared with experiments carried out on the ESR spectrum of 1-iminoxy -2,2,6,6-tetra(perdeuteromethyl)cyclohexane radical at -50% and 9 GHz.It has further been investigated how the noise is influenced