A discrete quasi-autoregressive moving average (QARMA) model and an equivalent impulse response (IR) description are established for linear continuous systems with internal and external point delays which are discretized through a sampler and zero-order-hold device. The QARMA-model is proved to differ from the standard autoregressive moving average (ARMA) models because of its infinite input memory caused by the delays. Based on the IR-model, a finite impulse response (FIR)-filter is proposed to approximate the input-output description under exponential stability of the unforced system. Its implementation is discussed by using fast filtering design tools.