Transfer Functions 1P 1Z Frequency Response
The Z transform of a system with a single pole at p1 and
a single zero at z1 along the real Z axis is given by:-
The frequency response is obtained by substituting
The applet below shows the frequency response of the system which is
also the Z transform along the unit circle in the Z plane.
The gray curve above the magenta lines show the response between 0 and
½ ws while the
gray curve above the green lines
show the response between ½ ws
and ws. Orange lines show
the phase variation. White disc shows the unit circle, black line
is the real z axis and orange line is the imaginary z axis. Pole is
shown by the "x" and the zero by an "o". When the "Theta" parameter is
zero the view is along the imaginary axis from the top. -90° corresponds
to a view along the real z axis from the left and +90° represents
a view along the real z axis from the right.
Note that having a pole near the unit circle produces a peak in the
response while having a zero on the unit circle produces a
zero in the response.
Setting Fn = 1 shows the unfolded spectrum between 0 and
2ws. Numerical values can be seen by changing wL.
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Copyright 2008 © Cuthbert A. Nyack.