Final answer:
Stage 3 NREM slow-wave sleep is where long, slow, high-amplitude brain waves, called delta waves, occur. This is the deep sleep stage and is marked by a significant slowing in heart rate and respiration.
Step-by-step explanation:
Long, slow, high-amplitude EEG waves are most commonly found during NREM stage 3 sleep, often referred to as deep sleep or slow-wave sleep. These waves, known as delta waves, have a frequency of less than 3 Hz, which is very low, and their amplitude is the highest among the brain wave patterns during sleep. During stage 3 sleep, a person's heart rate and respiration slow significantly, making it more difficult to awaken them.
Despite being called REM sleep, this stage actually involves brain waves very similar to those of an awake person and is not where the long, slow, high-amplitude waves are observed. REM is known for rapid eye movements, and the muscle systems are generally paralyzed except for those controlling circulation and respiration.