Suppose we measure the time-dependent spectrum of a single photon. That is, we first send the photon through a set of frequency filters (which we assume to have different filter frequencies but the same finite bandwidth Γ), and then record at what time (with some finite precision ∆t, and with some finite efficiency η) and after passing what filter the photon is detected. What is the POVM (PositiveOperator Valued Measure, the most general description of a quantum measurement) corresponding to such a measurement? We show how to construct the POVM in various cases, with special interest in the case Γ∆t 1 (time-frequency uncertainty still holds, even in that limit). One application of the formalism is to heralding single photons. We also find a Hong-Ou-Mandel type of interference effect with two photons entering a frequency filter.