This paper addresses the identification of finite impulse response (FIR) systems with both quantized and event-triggered observations. An event-triggered communication scheme for the binary-valued output quantization is introduced to save communication resources. Combining the empirical-measure-based identification technique and the weighted least-squares optimization, an algorithm is proposed to estimate the unknown parameter by full use of the received data and the not-triggered condition. Under quantized inputs, it is shown that the estimate can strongly converge to the real values and the estimator is asymptotically efficient in terms of the Cramér-Rao lower bound. Further, the limit of the average communication rate is derived and the tradeoff between this limit and the estimation performance is discussed. Moreover, the case of multi-threshold quantized observations is considered. Numerical examples are included to illustrate the obtained main results.

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