As can be seen from the pole-zero plot, when
,
the vector length
is minimized to . If is
small (),
and is dominant in , and
is maximized when
. In this
case, the system behaves like a band-pass filter which peaks at *approximately*
. Due to the second vector
, the actual peak frequency
is slightly lower than
. The precise peak
frequency can be found by solving

to be

which is very close to for small . The

where and are the

or

i.e., when , only half of the power contained in the signal can pass through the filter. To find , consider the two frequencies in the pole-zero plot

When is at either or , the vector in the denominator satisfies

and we have

Here we assumed as the second pole (in the 3rd quadrant) is farther away from both and than in the 2nd quadrant. We can now find approximately the bandwidth as