  Jointly training a speech enhancement (SE) front-end and an automatic speech
recognition (ASR) back-end has been investigated as a way to mitigate the
influence of \emph{processing distortion} generated by single-channel SE on
ASR. In this paper, we investigate the effect of such joint training on the
signal-level characteristics of the enhanced signals from the viewpoint of the
decomposed noise and artifact errors. The experimental analyses provide two
novel findings: 1) ASR-level training of the SE front-end reduces the artifact
errors while increasing the noise errors, and 2) simply interpolating the
enhanced and observed signals, which achieves a similar effect of reducing
artifacts and increasing noise, improves ASR performance without jointly
modifying the SE and ASR modules, even for a strong ASR back-end using a WavLM
feature extractor. Our findings provide a better understanding of the effect of
joint training and a novel insight for designing an ASR agnostic SE front-end.
