  Deep neural network (DNN) based end-to-end optimization in the complex
time-frequency (T-F) domain or time domain has shown considerable potential in
monaural speech separation. Many recent studies optimize loss functions defined
solely in the time or complex domain, without including a loss on magnitude.
Although such loss functions typically produce better scores if the evaluation
metrics are objective time-domain metrics, they however produce worse scores on
speech quality and intelligibility metrics and usually lead to worse speech
recognition performance, compared with including a loss on magnitude. While
this phenomenon has been experimentally observed by many studies, it is often
not accurately explained and there lacks a thorough understanding on its
fundamental cause. This paper provides a novel view from the perspective of the
implicit compensation between estimated magnitude and phase. Analytical results
based on monaural speech separation and robust automatic speech recognition
(ASR) tasks in noisy-reverberant conditions support the validity of our view.
