Converts cascade form filter coefficients to zeros, poles and gain.
CAS2ZP(c)
(z, p, k) = CAS2ZP(c)
c |
- |
A series. The filter coefficients in cascade form. |
A Nx3 array where the first column contains the zeros, the second column contains the poles and the third column contains the gain.
(z, p, k) = CAS2ZP(c) returns the zeros, poles and gain as three separate arrays.
c = {1, 1, -2, 0, -0.7, 0.1};
W1: cas2zp({1, 1, -2, 0, -0.7, 0.1})
W1 == {{0.0, 0.5, 1.0},
{2.0, 0.2}}
The 2nd order cascade filter coefficients represent the following Z transform:
The first column of W1 contains the zeros, the second column contains the poles and the third column is the gain.
c = {1, 1, -2, 0, -0.7, 0.1};
(z, p, k) = cas2zp(c);
z == {0.0, 2.0};
p == {0.5, 0.2};
k == 1.0;
The 2nd order cascade filter coefficients represent the following Z transform:
Same as the previous example except z contains the zeros, p contains the poles and k is the gain of the system.
CAS2ZP converts cascade coefficients to zeros, poles and gain of a discrete system where the input coefficients represent the following Z transform:
or:
where G is the system gain, b_{k} and a_{k} are the filter coefficients for the k^{th} stage.
The cascade filter coefficients are returned as a single column series with the coefficients in the following order:
{G, b_{10}, b_{11}, b_{12}, a_{11}, a_{12}, b_{20}, b_{21}, b_{22}, a_{21}, a_{22}, ... , b_{N0}, b_{N1}, b_{N2}, a_{N1}, a_{N2}}
CAS2ZP also works for analog cascade coefficients. In this case, the cascade system function becomes:
or equivalently:
See ZP2CAS to convert zeros, poles and gain to cascade form.