The capability to store light for extended periods of time enables optical cavities to act as narrow-band optical filters, whose linewidth corresponds to the cavitys inverse energy storage time. Here, we report on nonlinear filtering of an optical pulse train based on temporal dissipative Kerr solitons in microresonators. Our experimental results in combination with analytical and numerical modelling show that soliton dynamics enables storing information about the systems physical state longer than the cavitys energy storage time, thereby giving rise to a filter width that can be more than an order of magnitude below the cavitys intrinsic linewidth. Such nonlinear optical filtering can find immediate applications in optical metrology, low-timing jitter ultra-short optical pulse generation and potentially opens new avenues for microwave photonics.