  Quantum sensors are keeping the cutting-edge sensitivities in metrology.
However, for high-sensitive measurements of arbitrary signals, limitations in
linear dynamic range could introduce distortions when sensing the frequency,
magnitude and phase of unknown signals. Here, we overcome these limitations
with advanced sensing protocol that combines quantum phase-sensitive detection
with heterodyne readout. We present theoretical and experimental investigations
using nitrogen-vacancy centers in diamond, showing the ability to sense radio
signals with a 98 dB linear dynamic range, a 31 pT/Hz$^{1/2}$ sensitivity, and
arbitrary frequency resolution. Further, we perform the quantum-assisted
distortion-free audio signal (melody, speech) sensing with high fidelity. The
methods developed here could broaden the horizon for quantum sensors towards
applications in telecommunication, where high-fidelity and low-distortion at
multiple frequency bands within small sensing volumes are required.
