It is very broad question to ask.
In our company, we have been using PCB with pads coated in silver(HAL or tin coated).
However, the project in development is suffering from noise issue, so I am wondering if changing to gold plated pads may help in terms of noise issue.
With other factors kept the same, will there be any improvement theoretically?
From a noise point of view, gold plating of the PCB will hardly make any difference. The question is very general, so this is the short general answer.
Gold plating is an additional thin gold coating of few tens of nanometers on top of the external metal layers. It can be beneficial because it avoids oxidation of the pads and thus limits faulty contacts. Gold plating can also be used to facilitate direct wire-bonding to the PCB, in particular with pure gold wires.
Depends on the application, there are two problems that affect electrical signals.
1) Resistance - Gold will have lower resistance and better soldering properties.
2) Seebeck effects - PCB solder junctions turn into small thermocouples which can make uV's of voltage offset. These offsets are depended on the temperature and the metals involved. Metals must be similar to avoid the seebeck effect. I don't know if this would be worse for gold but its something to be aware of. These affects would be around DC in frequency and would not affect faster systems.
http://circuitcellar.com/cc-blog/the-basics-of-thermocouples/
If your looking to lower noise, changing the PCB metal is probably not the best place to be looking for noise reduction for analog circuits.
