Converts zeros, poles and gain to transfer function form.
ZP2TF(z, p, k)
(b, a) = ZP2TF(z, p, k)
z |
- |
A series, the zeros. |
p |
- |
A series, the poles. |
k |
- |
Optional. A scalar, the gain. Defaults to 1.0 |
A Nx2 array where the first column contains the numerator coefficients and the second column contains the denominator coefficients.
(b, a) = ZP2TF(z, p, k) returns the numerator and denominator coefficients in two separate series.
W1: zp2tf({0}, {0.5}, 1)
W1 == {{1, 0}, {1, -0.5}}
W1 contains two columns, where the first column is {1, 0}, the numerator coefficients and the second column is {1, -0.5}, the denominator coefficients. The coefficients represent the system:
(b, a) = zp2tf({0}, {0.5}, 1)
b == {1, 0}
a == {1, -0.5}
Same as above except the coefficients are returned in two separate variables.
z = {0.0, 2.0};
p = {0.5, 0.2};
k = 1.0;
(b, a) = zp2tf(z, p, k);
b == {1, -2, 0};
a == {1, -0.7, 0.1};
The coefficients represent the system:
For zp2tf(z, p, k), the input series represent the zeros, poles and gain of the rational polynomial
z^{ } |
=^{ } |
e^{ jω} complex frequency |
N |
= |
number of numerator terms |
M |
= |
number of denominator terms |
ZP2TF returns the numerator coefficients b(z) and the denominator coefficients a(z).
ZP2TF also works for continuous systems with a transfer function in decreasing powers of s.
See TF2ZP to convert a continuous S plane transfer function to zeros, poles and gain.
See TF2ZPK to convert a discrete Z plane transfer function to zeros, poles and gain.