  We extend the Fourier transform based method for the analysis of galaxy
redshift surveys of Feldman, Kaiser & Peacock (1994: FKP) to model
luminosity-dependent clustering. In a magnitude limited survey, galaxies at
high redshift are more luminous on average than galaxies at low redshift.
Galaxy clustering is observed to increase with luminosity, so the inferred
density field is effectively multiplied by an increasing function of radius.
This has the potential to distort the shape of the recovered power spectrum. In
this paper we present an extension of the FKP analysis method to incorporate
this effect, and present revised optimal weights to maximize the precision of
such an analysis. The method is tested and its accuracy assessed using mock
catalogues of the 2-degree field galaxy redshift survey (2dFGRS). We also show
that the systematic effect caused by ignoring luminosity-dependent bias was
negligible for the initial analysis of the 2dFGRS of Percival et al. (2001).
However, future surveys, sensitive to larger scales, or covering a wider range
of galaxy luminosities will benefit from this refined method.
