Connect mobile/tablet to TV - Full HD?

[ajf]

I've got a Galaxy S3 and Galaxy Note 8.
I purchased one of the MHL cables that uses the mini usb to connect to the HDMI port.

It works fine to a degree, but only seems to just mirror the screen and resolution of the actual device.

Is there any way of getting the devices connected to the TV and run them at 1080p?
The TV is a basic non smart Samsung so doesn't have the latest sharing technology.

 

[BigDannyO]

Do you have the official cable?

I used one with my S3 to my Panasonic plasma and it showed 1080p content at 1080p.

Can't remember but I think the mirror of the desktop would have been at the phones native res, so 720p-ish?