A new technique for Brillouin optical correlation domain analysis is proposed and demonstrated, in which the pump and signal waves are drawn from the filtered amplified spontaneous emission of an erbium-doped fiber amplifier. An estimated spatial resolution of 3.3 mm is obtained using a 33 GHz-wide source. The reconstruction of the Brillouin gain line and the recognition of a localized hot spot are demonstrated in a proof-of-concept experiment. Unlike phase-coded correlation domain analysis methods, the proposed scheme is not restricted by the bandwidth of available electro-optic modulators or pattern generators. Resolution is scalable to less than one millimeter.