Quantum sensors are keeping the cutting-edge sensitivities in metrology. However, for highsensitive 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 the 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.