We present a new operator method in the Heisenberg representation to obtain the signal of parity measurement within a lossless SU(1,1) interferometer. Based on this method, it is convenient to derive the parity signal directly in terms of input states, including general Gaussian or non-Gaussian state. As applications, we revisit the signal of parity measurement within an SU(1,1) interferometer when a coherent or thermal state and a squeezed vacuum state are considered as input states. In addition, we also obtain the parity signal of a Fock state when it passes through an SU(1,1) interferometer, which is also a new result. Therefore, the operator method proposed in this work may bring convenience to the study of quantum metrology, particularly the phase estimation based on an SU(1,1) interferometer.
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