Electronic – ADXL354 Power Sequencing Sources and LDO’s

A simple battery backup IC will do what you want.

Essentially, a comparator samples two voltage inputs, the main power, and a backup power supply (Batteries). Based on that, two cascading inverters paired with two p-channel fets power the circuit at Vo, while two n-channel fets are used as open-drain outputs. Pull them up with a resistor, and they are the perfect interrupt source for your arduino.

The specific one shown is the ICL7673, but it's maximum current is 38mA. It's designed for rtc and ram with a coincell, but an extra pair of P-channels can be used to increase the current.

There are other battery backup or power switches which will do higher current builtin.

There is no real difference between an analogue power supply and a digital power supply. They are separated because the digital power supply will supply current to digital switches which will switch on and off rapidly, putting large current demand spikes onto the power line, and hence cause momentary voltage drops and spikes on the line - these spikes are managed by decoupling capacitors local to the switching devices, and bulk capacitance at the power supply.

By keeping the two supply lines separate the circuit designer can isolate these current spikes from analogue circuitry which may be affected by small voltage drops - for example if the supply is used as a reference for an A2D. Often the two supplies are fed from the same source, but the analogue supply may have a small RC or inductive filter in line to remove digital noise present at the source.

So yes, the 3.3v pin of the STM32F4-discovery board could be used as an analog power source. I would just add a small series resistor (less than 0.05V drop at the current you are using) and additional capacitance to ground - to give a first order low pass filter frequency of about 1KHz - or whatever you deem appropriate.