I want to do some testing but I don't want to burn-out my chip. Would it be safe to take a PWM signal from a digital output pin and route it directly to one of the analog inputs or do I need a resistor?
Neither of the two. You'll need some sort of smoothing, since the pwm signal is on-off-on-off. Check out GrumpyMike's website: PWM
Joachim
Would it be safe to take a PWM signal from a digital output pin and route it directly to one of the analog inputs
Yes it is safe, no resistor needed, if that is what you are worrying about. However, as pointed out by Joachim it will not do what you expect as a PWM signal is really digital.
I am hoping to be able to use the full 5V range from the PWM signal. The analog signal derived from PWM would maybe vary from 0-25Hz. Is it reasonable to use a really low value resistor in the RC filter, say 10ohms with a 150uF cap to minimize the voltage drop and get a 100Hz cut-off frequency?
Is it reasonable to use a really low value resistor in the RC filter, say 10ohms with a 150uF
No it is not reasonable. The reason is that the arduino can't stand the current that it would require, it would damage the arduino.
What are you feeding the voltage into? That is what output impedance requirements do you have?
On the face of it, it sounds like you need a much higher order filter than a simple RC, one involving op amps. The other thing you could try is increasing the PWM frequency. Do a search to find out what register to poke.
I want to generate a 0-25Hz analog signal (as close to 0-5V as possible, but I can compromise) from the PWM to feed into an analog pin on the Arduino. Basically I want to modulate the frequency of another oscillator using this analog signal as a control.