Sun,

Erik's response is dead on correct.

A frequent occurrence in signal processing applications is that one wishes to measure an ac component (or range of components) of a signal, or a dc component of a signal, but for some reason the signal may have both components present. A filter can decrease the contribution of the undesired component prior to measuring it. For example, if a dc value is desired of a signal which also has an ac component, the signal should be passed through a low-pass filter prior to measuring it. Likewise, if an ac component is desired pass the signal through a high-pass filter. Now, these two filters have general 'shapes' in the frequency domain, but many implementations depending on the precise nature of the 'shape' desired.

Since your original question related to a PID, I'm guessing you want to understand how to smooth a feedback signal before applying it to a PID, or how to implement a PID as a filter. I'll give you the first here, but the second is a bit tricky as a purely linear implementation is fraught with faults in the real world. This is an easy, first order difference equation that implements a low pass filter as an infinte impulse response (IIR) filter -

y(n) = b*y(n-1) + a*x(n)

where n is an index (n is the present value, n-1 is the value from the last iteration),
x is the input
y is the output
a & b are cofficients whose sum is one individually greater than zero. To make the filter have a fast response make a greater than b. To make the filter have a slower response, make b greater than a.

If after reading this, you still wish to implement a linear PID, I'd be happy to work through it with you in this thread.

Cheers,

Bruce