Re: audio amplifier
Here are a few:
1. Power output -- How much power is to be delivered to what size load?
2. Gain -- How much input signal is necessary to produce a certain output?
3. Bandwidth -- What frequencies at the input will be reproduced in the output?
4. Linearity -- Is the gain of the amp constant throughout the bandwidth?
5. Power Supply -- What is the maximum voltage amplitude desired at the load and how much current will the supply need to provide to see that amplitude at the load?
6. Size -- Is this a stand-alone amp, or will it need to be incorporated into another system that limits the real estate available?
7. Harmonic Distortion -- How much extraneous information will there be at the output? (All amps produce extra power across the load at frequencies that are integer multiples (harmonics) of the input signal frequencies. This extra (usually wasted) power requires an even larger power supply for the amp, assuming you don't want reduced power output at the frequencies of interest.)
There's a little to get you started.