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Pulse Doppler radar needs accurate measurement of the quadrature sampling system error for error correction to reduce false alarm rate and improve the clutter suppressing performance and the improvement factor. This paper firstly introduces the discrete Hilbert transform to estimate the relative amplitude error and phase error of quadrature sampling system using coherent testing signal. The error function with respect to each sample is derived theoretically. Computer simulation shows that the theoretical results are effective and accurate. The results can be used to evaluate and correct the errors in the quadrature sampling system to contribute to suppress the background moving clutter and reduce false alarm rate for the pulse Doppler radar.