Quantum noise sets a fundamental limit to the sensitivity of high-precision measurements. Suppressing it can be achieved by using non-classical states and quantum filters, which modify both the noise and signal response. We find a novel approach to realising quantum filters directly from their frequency-domain transfer functions, utilising techniques developed by the quantum control community. It not only allows us to construct quantum filters that defy intuition, but also opens a path towards the systematic design of optimal quantum measurement devices. As an illustration, we show a new optical realisation of an active unstable filter with anomalous dispersion, proposed for improving the quantum-limited sensitivity of gravitational-wave detectors.
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