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In this paper, we show that convolutional neural networks can be directly applied to temporal low-level acoustic features to identify emotionally salient regions without the need for defining or applying utterance-level statistics. We show how a convolutional neural network can be applied to minimally hand-engineered features to obtain competitive results on the IEMOCAP and MSP-IMPROV datasets. In addition, we demonstrate that, despite their common use across most categories of acoustic features, utterance-level statistics may obfuscate emotional information. Our results suggest that convolutional neural networks with Mel Filterbanks (MFBs) can be used as a replacement for classifiers that rely on features obtained from applying utterance-level statistics.