  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 $k\ge 0.2 h$ 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. 
Power Spectrum Analysis of the ESP Galaxy Redshift Survey