Modulation filtering is a technique for filtering slowly-varying envelopes of frequency subbands of a non-stationary signal, ideally without affecting the signal's phase and fine-structure. Coherent modulation filtering is a potentially more effective subtype of such techniques where subband envelopes are determined through demodulation of the subband signal with a coherently detected subband carrier. In this paper we propose a coherent modulation filtering technique based on detecting the instantaneous frequency of a subband from its time-frequency representation. We show that coherent modulation filtering imposes a new bandlimiting constraint on the modulation product plus the ability to recover arbitrarily chosen envelopes and carriers from their modulation product. We show that a carrier estimate based on the time-varying spectral center-of-gravity satisfies the bandlimiting condition as well as Loughlin's previously
derived bandlimiting constraint on the instantaneous frequency of carrier. These bandwidth constraints lead to effective and distortion-free modulation filters, offering new approaches for potential signal modification. The spectral center-of-gravity does not satisfy the condition on arbitrary recovery, however, which somewhat limits the flexibility of coherent modulation filtering. Demonstrations are provided with speech signals.