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This study addresses the problem of detecting signals characterised by a discontinuous presence in the detection window. This situation is of particular interest for applications of spectrum sensing in cognitive radio networks where, on the one hand, the sampling frequency may be limited by hardware capabilities and, on the other hand, the signal to be detected may be bursty with a burst duration comparable to or lower than the minimum sampling period. Modified expressions are derived for the detection probability of two popular detectors - energy detector and largest eigenvalue test - in the presence of discontinuous signals. The new expressions, adapted as a function of the signal occupancy rate, provide an accurate estimation of the detection probability under this scenario and allow a more careful selection of the decision threshold.