Periodic breathing is the term for short bouts of unusual respiration in newborns and infants. In its most usual form, the baby will breathe really fast for a few seconds, pause for a few seconds, return to normal breathing, and then start the cycle again. This is common and not something to worry about.
Periodic breathing occurs in about 80% of newborns, decreasing over the first year of life. The pauses in breathing may be accompanied by bradycardia. In some cases it may occur when the infant is awake; this is unusual, but not a concern. Breath pauses of up to 12 seconds occur in some cases, and as long as the baby resumes breathing on their own this is not cause for concern... but you should probably let your pediatrician know; I have never met your kid, and IANAD.
To be clear, neither periodic breathing, sputtering, gurgles, coughs, or turning a bit red are serious concerns. However, the pauses in breathing should not last much more than 10 seconds and the baby should be able to start breathing again on their own. The baby should never change color due to lack of oxygen. If your baby changes color to become very pale, blue, or grayish, that signals a medical emergency, and requires immediate medical attention.
Periodic breathing in adults may be the sign of a serious medical condition (e.g., congestive heart failure) or sleep apnea. If you are breathing funny when you sleep, check with your doctor.