In a filter response plot, is H(w) or H(f) is frequency response and w the frequency?

Question

when w is used in terms of pi and 2pi, what does that represent in terms of true freq? (Mhz?)

so does an w of 2pi, means f = 1, so is that 1 Hz?

Answer 1

w (small-case omega) is radian frequency in units of radians per second

f is frequency in units of cycles per second, or Hertz.

There are 2*pi radians in a complete cycle (around a circle), therefore:
2 * pi * f = w

.

Answer 2

w = 2*pi*f where f = frequency in Hz. w is sometimes referred to as circular frequency. It is used because f almost always appears multiplies by 2*pi in trig arguments that have to do with Fourier analysis.

If you use H(f), be carfeful to put in the 2*pi's as appropriate. It is easier to use H(w) and plot it against w/(2*pi)

Answer 3

w is angular frequency in radian per second
f is cyclic frequency in cycles per sec
1 cycle = 2pi radians
so
w = 2 pi f
H(f) or H(w) is the transfer function of a linear system
input X(f)
output Y(f) = H(f) X(f)