An "excessively tired" grandfather who shook his baby grandson for six seconds, leading to the infant's death, has been jailed for seven-and-a-half years.

Perth man Wayne William Downing was the primary caregiver for 3-month-old Noah in May 2016.

The 48-year-old told police he has fallen asleep on the couch when Noah woke up in his room and began crying.

The frustrated and "excessively tired" grandfather went into the room, saying he gave Noah "just a little shake" for about six seconds before putting him back down.

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The infant's mother returned home to find Noah cold, blue and unresponsive.

Noah had suffered traumatic injuries to his brain and spine.

Downing was initially charged with murder but pleaded guilty to the lesser offence of manslaughter.

A judge said Downing shook Noah in the irrational hope that "doing so would make him fall asleep".

"As soon as I put him down I realised what I'd done ... I was just trying to go off to sleep and to get some sleep."

Wayne Downing and his grandson Noah, who passed away.
Wayne Downing and his grandson Noah, who passed away.

But Downing did not attempt to seek medical help after realising Noah was injured.

Downing only admitted to shaking the baby during his second interview with police, the Supreme Court of Western Australia heard.

Justice Anthony Derrick accepted that Downing loved Noah and had not intended to hurt or kill him.

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"You shook Noah out of frustration, and in the irrational and forlorn hope that doing so would make him be quiet and fall asleep," he said.

"Further, there is no suggestion that you had ever previously subjected Noah to any form of abuse or ill-treatment."

However, Justice Derrick said he failed to seek medical assistance, which was not the right thing to do.

"I recognise that even if you had made a more immediate attempt to seek assistance for Noah, this may not have any difference to the outcome for him, given the extent of his injuries," he said.

"However, you could not have known this and the right thing to do would have been to immediately seek help."

Downing was supported in court by his family, including Noah's mother.

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