Probability of detection P_D against probability of false alarm P_FA for the detection methods in the numerical experiment described in Sect. 3. The sources are assumed to have an intensity a_i at the ith frequency given by a_i = (ν_i/ν₁)^αa₁, with a₁ = 0.5. Four values for α are considered, α = 3,1,0.5,0.05. The results are shown for the different methods: the weighted matched filter (WMF), the multi-frequency matched filter (MMF), the uniformly weighted matched filter (UWMF) and the average matched filter (AMF). The MMF is used as benchmark because it has the best theoretical detection performance. The UWMF shows the worst possible results obtainable with the WMF approach. The AMF shows which results are obtainable when the maps are simply averaged. A method is superior to another one when for a fixed P_FA the corresponding P_D is greater (for a given method, the relation P_D to P_FA should always be well above a 45° straight line, the dashed line in the figure). With increasing α, the behaviour of MMF and WMF becomes similar. For an α close to zero, the MMF and AMF show a very similar performance.