Vocal communicators such as humans and songbirds readily recognize individual vocalizations, even in distracting auditory environments. This perceptual ability is likely subserved by auditory neurons whose spiking responses to individual vocalizations are minimally affected by background sounds. However, auditory neurons that produce background-invariant responses to vocalizations in auditory scenes have not been found. Here, we describe a population of neurons in the zebra finch auditory cortex that represent vocalizations with a sparse code and that maintain their vocalization-like firing patterns in levels of background sound that permit behavioral recognition. These same neurons decrease or stop spiking in levels of background sound that preclude behavioral recognition. In contrast, upstream neurons represent vocalizations with dense and background-corrupted responses. We provide experimental evidence suggesting that sparse coding is mediated by feedforward suppression. Finally, we show through simulations that feedforward inhibition can transform a dense representation of vocalizations into a sparse and background-invariant representation.