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We propose a new study of multichannel time-domain noise reduction filters where we decompose the noise-free microphone array observations into two components: the first is correlated with the target signal and perfectly coherent across the sensors while the second consists of residual interference. Then, alternative formulations of well known time-domain filters, namely, the minimum variance distortionless response (MVDR), the linearly constrained minimum variance (LCMV), the multichannel tradeoff, and Wiener filters are given. Besides, the performance of these time-domain filters are analytically investigated and new insights are presented. Numerical results are finally provided to corroborate our study.