Most FIRs are linear-phase filters; when a linear-phase filter is desired, a FIR is usually used.
"Linear Phase" refers to the condition where the phase response of the filter is a linear (straight-line) function of frequency (excluding phase wraps at +/- 180 degrees). This results in the delay through the filter being the same at all frequencies. Therefore, the filter does not cause "phase distortion" or "delay distortion". The lack of phase/delay distortion can be a critical advantage of FIR filters over IIR and analog filters in certain systems, for example, in digital data modems.
FIR filters are usually designed to be linear-phase (but they don't have to be.) A FIR filter is linear-phase if (and only if) its coefficients are symmetrical around the center coefficient, that is, the first coefficient is the same as the last; the second is the same as the next-to-last, etc. (A linear-phase FIR filter having an odd number of coefficients will have a single coefficient in the center which has no mate.)
The formula is simple: given a FIR filter which has N taps, the delay is: (N - 1) / (2 * Fs), where Fs is the sampling frequency. So, for example, a 21 tap linear-phase FIR filter operating at a 1 kHz rate has delay: (21 - 1) / (2 * 1 kHz) = 10 milliseconds.
Non-linear phase, of course. ;-) Actually, the most popular alternative is "minimum phase". Minimum-phase filters (which might better be called "minimum delay" filters) have less delay than linear-phase filters with the same amplitude response, at the cost of a non-linear phase characteristic, a.k.a. "phase distortion".
A lowpass FIR filter has its largest-magnitude coefficients in the center of the impulse response. In comparison, the largest-magnitude coefficients of a minimum-phase filter are nearer to the beginning .
For an N-tap FIR filter with coefficients h(k), whose output is described by:
y(n) = h(0)x(n) + h(1)x(n-1) + h(2)x(n-2) + ... h(N-1)x(n-N-1),
the filter's Z transform is:
H(z) = h(0)z-0 + h(1)z-1 + h(2)z-2 + ... h(N-1)z-(N-1) , or
The variable z in H(z) is a continuous complex variable, and we can describe it as: z = r·ejw, where r is a magnitude and w is the angle of z. If we let r = 1, then H(z) around the unit circle becomes the filter's frequency response H(jw). This means that substituting ejw for z in H(z) gives us an expression for the filter's frequency response H(w), which is:
H(jw) = h(0)e-j0w + h(1)e-j1w + h(2)e-j2w + ... h(N-1)e-j(N-1)w , or
Using Euler's identity, e-ja = cos(a) - jsin(a), we can write H(w) in rectangular form as:
H(jw) = h(0)[cos(0w) - jsin(0w)] + h(1)[cos(1w) - jsin(1w)] + ... h(N-1)[cos((N-1)w) - jsin((N-1)w)] , or
Yes. For an N-tap FIR, you can get N evenly-spaced points of the frequency response by doing a DFT on the filter coefficients. However, to get the frequency response of the filter at any arbitrary frequency (that is, at frequencies between the DFT outputs), you will need to use the formula above.