Warning: The video above is graphic.

BATON ROUGE, La. -- Outrage is growing over the police shooting of a black man in Louisiana with new cell phone video showing a different perspective of the deadly encounter between Alton Sterling and two Baton Rouge officers.

As hundreds protested Wednesday night at the convenience store where the shooting took place, a Baton Rouge official said the officers involved in the shooting believe their actions were justified, reports CBS News correspondent David Begnaud.

The second video, taken from a closer angle, appears to show Sterling pinned down by two Baton Rouge police officers. Moments later, Sterling is shot multiple times in the chest and back. The 37-year-old died at the scene.

"When you see this happen on camera again and again and again, it's like wow," one protester said.

Abdullah Muflahi recorded the video in the parking lot of his convenience store.

"He didn't know why they were there, why they came to get him," Muflahi said.

Federal investigators are examining the deadly encounter at the request of Louisiana Gov. John Bel Edwards.

"We all learned lessons from what was done elsewhere in the country over the last several years and we're trying to be as proactive as possible," Edwards said.

The shooting happened early Tuesday morning when Baton Rouge police department officers Blane Salamoni and Howie Lake II responded to a disturbance call involving Sterling, who was reportedly armed.

Sterling has a lengthy police record. Past charges include a felony drug offense and aggravated assault.

District Attorney Hillar Moore said Lake and Salamoni may have acted within their rights.

"This is potentially a state authorized killing," Moore said. "It gives law enforcement officers the authority and mandates them to kill when in defense of themselves or others."

Sterling's 15-year-old son, Cameron, sobbed as his family addressed reporters during a press conference Wednesday. Quinyetta McMillon is his mother.

"As a parent one of the greatest fears is to see your child hurt and know there's nothing you can do about it," McMillon said.

Both officers involved were wearing body cameras that fell off during the shooting, but we are told the audio will be crucial to the investigation.