Displays a Pole-Zero plot of a S
SPLANE(b, a)
b |
- |
A series. The numerator (i.e. zero) coefficients in descending powers of s. |
a |
- |
A series. The denominator (i.e. pole) coefficients in descending powers of s. |
SPLANE(z, p, g)
z |
- |
A series. The zeros of the S |
p |
- |
A series. The poles of the S |
g |
- |
A scalar. The gain of the system. |
SPLANE(c)
c |
- |
A series. The system coefficients in cascaded biquad form. If c contains 2 columns, the coefficients are assumed to be in direct form, where the first column is b and the second column is a. |
An XY series, where each pole is plotted as a light red "x" and each zero is plotted as a black "o".
W1: splane({1}, {1, 0.5})
Displays the s plane with a single pole at s = -0.5. The input is given as a system function in descending terms of s.
W1: splane({0}, {-0.5}, 1)
Displays the same plot as above. The input is given in terms of zeros and poles.
z = roots({1, 2, 0});
p = roots({1, 0.7, 0.1});
splane(z, p, 1);
Displays two real poles and two zeros in the current Window. This result is identical to:
splane({1, 2, 0}, {1, 0.7, 0.1})
For splane(b, a), the input series
represent the terms of the rational polynomial
s |
= |
jω complex frequency |
N |
= |
number of numerator terms |
M |
= |
number of denominator terms |
For splane(z, p, g), the gain term must be present, but it does not effect the resulting plot.
For splane(c),
the input c is assumed to be a single column
of coefficients in cascaded
or equivalently:
where G is the system gain, b_{k} and a_{k} are the filter coefficients for the k^{th} stage.
If c contains 2 columns, the coefficients are assumed to be in direct form, where the first column is b and the second column is a.
The aspect ratio of the window is set to square to preserve a circular unit circle.
Each pole is plotted as a light red "x" and each zero as a black "o". The unit circle is displayed as a solid circle in the current series color. Axes lines are also drawn through the origin.
Multiple zeros and poles are labeled with a multiplicity number to the upper right of the symbol.
See ZPLANE for a Pole-Zero plot of a discrete system.