  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.
