Electron spin resonance (ESR) spectra of alanine detectors irradiated to absorbed doses below 5 Gy are affected by a varying non-linear background which mainly influences the lower limit of detection in alanine/ESR dosimetry. A mathematical method based on fast Fourier transform is described capable of filtering simultaneously background and noise in the frequency domain of ESR spectra. It provides clearer alanine/ESR signals down to 50 mGy. Even in non-irradiated but long-term stored alanine detectors an ESR signal could be observed similar to irradiated alanine (pre-signal). A linear ESR signal vs absorbed dose relationship was found above 200 mGy, after correction for background and pre-signal. The number of repeated ESR read-out cycles and hence the time required for a precise and reliable low-dose evaluation have significantly been reduced. The method has been worked out for the therapy-level dosimetry range and tested on a Bruker ESP 300 and for comparison Bruker EMS 104 ESR spectrometer.