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Quantum sensors are known for their high sensitivity in sensing applications. However, this sensitivity often comes with severe restrictions on other parameters which are also important. Examples are that in measurements of arbitrary signals, limitation in linear dynamic range could introduce distortions in magnitude and phase of the signal. High frequency resolution is another important feature for reconstructing unknown signals. Here, we demonstrate a distortion-free quantum sensing protocol that combines a quantum phase-sensitive detection with heterodyne readout. We present theoretical and experimental investigations using nitrogen-vacancy centers in diamond, showing the capability of reconstructing audio frequency signals with an extended linear dynamic range and high frequency resolution. Melody and speech based signals are used for demonstrating the features. The methods could broaden the horizon for quantum sensors towards applications, e.g. telecommunication in challenging environment, where low-distortion measurements are required at multiple frequency bands within a limited volume. 1e1e36bf2d