Animal communication sounds exhibit complex temporal structure because of the amplitude fluctuations that comprise the sound envelope. In human speech, envelope modulations drive synchronized activity in auditory cortex (AC), which correlates strongly with comprehension (Giraud and Poeppel, 2012; Peelle and Davis, 2012; Haegens and Zion Golumbic, 2018). Studies of envelope coding in single neurons, performed in nonhuman animals, have focused on periodic amplitude modulation (AM) stimuli and use response metrics that are not easy to juxtapose with data from humans. In this study, we sought to bridge these fields. Specifically, we looked directly at the temporal relationship between stimulus envelope and spiking, and we assessed whether the apparent diversity across neurons' AM responses contributes to the population representation of speech-like sound envelopes. We gathered responses from single neurons to vocoded speech stimuli and compared them to sinusoidal AM responses in auditory cortex (AC) of alert, freely moving Mongolian gerbils of both sexes. While AC neurons displayed heterogeneous tuning to AM rate, their temporal dynamics were stereotyped. Preferred response phases accumulated near the onsets of sinusoidal AM periods for slower rates (<8 Hz), and an over-representation of amplitude edges was apparent in population responses to both sinusoidal AM and vocoded speech envelopes. Crucially, this encoding bias imparted a decoding benefit: a classifier could discriminate vocoded speech stimuli using summed population activity, while higher frequency modulations required a more sophisticated decoder that tracked spiking responses from individual cells. Together, our results imply that the envelope structure relevant to parsing an acoustic stream could be read-out from a distributed, redundant population code.SIGNIFICANCE STATEMENT Animal communication sounds have rich temporal structure and are often produced in extended sequences, including the syllabic structure of human speech. Although the auditory cortex (AC) is known to play a crucial role in representing speech syllables, the contribution of individual neurons remains uncertain. Here, we characterized the representations of both simple, amplitude-modulated sounds and complex, speech-like stimuli within a broad population of cortical neurons, and we found an overrepresentation of amplitude edges. Thus, a phasic, redundant code in auditory cortex can provide a mechanistic explanation for segmenting acoustic streams like human speech.