Phasor plots of the fluorescence intensity decay (plots of the Fourier sine transform vs. the Fourier cosine transform, for one or several angular frequencies) are being increasingly used, namely in fluorescence lifetime imaging microscopy (FLIM) of cells, tissues and surfaces, but are also relevant for the characterization of homogeneous (e.g. solution) systems. In this work, the construction of the phasor plot using time domain data is discussed, including the effect of the instrument response function (IRF). A deconvolution method in the Fourier space is described. The results obtained are applied to fluorescence decays of aqueous fluorescein (basic form) in the presence of concentrated potassium iodide. The effect of the impulse is clearly shown, in accordance with model predictions. Deconvolution in the Fourier space works well for lifetimes at least one order of magnitude higher than the IRF time width.