Conveniently it happened again this morning, so I took a few minutes to look at the problem some more.

First, the noise itself. It appears to be made up of two components, one is a very clean, even and constant static. The second component is electronics noise from within the empeg, you can here the CPU chirping away and you can hear a burst of noise when the disk is spun up and read.

The level of noise doesn't vary with the volume control.

It is present in the background when both the tuner and MP3 player are active. It doesn't change at all when you change radio stations.

The noise goes away when the player is in sleep mode (i.e. plugged in but turned off). The noise can't be muted using the tuner mute.

The noise starts before the "radio module enabled" message during boot.

Rebooting using Hijack doesn't make the noise go away. If you force the player into AC mode and reboot the noise is quieter, but still there, in AC mode.
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Remind me to change my signature to something more interesting someday