This hum problem is is an issue your dac, my suggestion is replace the DAC or don't power your pi off.
The Raspberry Pi is an extremely low power device, you won't be making any noticeable cost savings on your electricity bill by powering off the Pi when not in use so just leave it on.
The Raspberry Pi is an extremely low power device, you won't be making any noticeable cost savings on your electricity bill by powering off the Pi when not in use so just leave it on.