This work presents a spatial filtering method for the estimation of atrial fibrillation activity in the cutaneous electrocardiogram. A linear extraction filter is obtained by maximising the extractor output power on the significant spectral support of the signal of interest. An iterative procedure based on a quasi-maximum likelihood estimator is proposed to jointly estimate the significant spectral support and the extraction filter. Compared with a previously proposed spatio-temporal blind source separation method, our approach yields an improved atrial activity signal estimate as quantified by a higher spectral concentration of the extractor output. The proposed methodology can readily be adapted to signal extraction problems in other application domains.