We measure the power spectrum of the galaxy distribution in the ESO Slice Project ( ESP ) galaxy redshift survey .
We develope a technique to describe the survey window function analytically , and then deconvolve it from the measured power spectrum using a variant of the Lucy method .
We test the whole deconvolution procedure on ESP mock catalogues drawn from large N–body simulations , and find that it is reliable for recovering the correct amplitude and shape of P ( k ) at k > 0.065 h Mpc ^ { -1 } .
In general , the technique is applicable to any survey composed by a collection of circular fields with arbitrary pattern on the sky , as typical of surveys based on fibre spectrographs .
The estimated power spectrum has a well–defined power–law shape k ^ { n } with n \simeq - 2.2 for k \geq 0.2 h Mpc ^ { -1 } , and a smooth bend to a flatter shape ( n \simeq - 1.6 ) for smaller k ’ s .
The smallest wavenumber , where a meaningful reconstruction can be performed ( k \sim 0.06 h Mpc ^ { -1 } ) , does not allow us to explore the range of scales where other power spectra seem to show a flattening and hints for a turnover .
We also find , by direct comparison of the Fourier transforms , that the estimate of the two–point correlation function \xi ( s ) is much less sensitive to the effect of a problematic window function as that of the ESP , than the power spectrum .
Comparison to other surveys shows an excellent agreement with estimates from blue–selected surveys .
In particular , the ESP power spectrum is virtually indistinguishable from that of the Durham-UKST survey over the common range of k ’ s , an indirect confirmation of the quality of the deconvolution technique applied .