Context. Atmospheric properties of F-, G- and K-type stars can be measured by spectral model fitting or with the analysis of equivalent width (EW) measurements. These methods require data with good signal-to-noise ratios (S/Ns) and reliable continuum normalisation. This is particularly challenging for the spectra we have obtained with the CORALIE échelle spectrograph for FGK stars with transiting M-dwarf companions. The spectra tend to have low S/Ns, which makes it difficult to analyse them using existing methods. Aims. Our aim is to create a reliable automated spectral analysis routine to determine T_eff, [Fe/H], V sini from the CORALIE spectra of FGK stars. Methods. We use wavelet decomposition to distinguish between noise, continuum trends, and stellar spectral features in the CORALIE spectra. A subset of wavelet coefficients from the target spectrum are compared to those from a grid of models in a Bayesian framework to determine the posterior probability distributions of the atmospheric parameters. Results. By testing our method using synthetic spectra we found that our method converges on the best fitting atmospheric parameters. We test the wavelet method on 20 FGK exoplanet host stars for which higher-quality data have been independently analysed using EW measurements. We find that we can determine T_eff to a precision of 85 K, [Fe/H] to a precision of 0.06 dex and V sini to a precision of 1.35 km s⁻¹ for stars with V sini ≥ 5 km s⁻¹. We find an offset in metallicity ≈− 0.18 dex relative to the EW fitting method. We can determine log g to a precision of 0.13 dex but find systematic trends with T_eff. Measurements of log g are only reliable enough to confirm dwarf-like surface gravity (log g ≈ 4.5). Conclusions. The wavelet method can be used to determine T_eff, [Fe/H], and V sini for FGK stars from CORALIE échelle spectra. Measurements of log g are unreliable but can confirm dwarf-like surface gravity. We find that our method is self consistent, and robust for spectra with S∕N ⪆ 40.