Understanding how single cortical neurons discriminate between sensory stimuli is fundamental to providing a link between cortical neural responses and perception. The discrimination of sensory stimuli by cortical neurons has been intensively investigated in the visual and somatosensory systems. However, relatively little is known about discrimination of sounds by auditory cortical neurons. Auditory cortex plays a particularly important role in the discrimination of complex sounds, e.g., vocal communication sounds. The rich dynamic structure of such complex sounds on multiple time scales motivates two questions regarding cortical discrimination. How does discrimination depend on the temporal resolution of the cortical response? How does discrimination accuracy evolve over time? Here we investigate these questions in field L, the analogue of primary auditory cortex in zebra finches, analyzing temporal resolution and temporal integration in the discrimination of conspecific songs (songs of the bird's own species) for both anesthetized and awake subjects. We demonstrate the existence of distinct time scales for temporal resolution and temporal integration and explain how they arise from cortical neural responses to complex dynamic sounds.