Model system defined by zeros and poles of discrete transfer function
Simulink / Discrete
The Discrete ZeroPole block models a discrete system defined by the zeros, poles, and gain of a zdomain transfer function. This block assumes that the transfer function has the following form:
$$H(z)=K\frac{Z(z)}{P(z)}=K\frac{(z{Z}_{1})(z{Z}_{2})\mathrm{...}(z{Z}_{m})}{(z{P}_{1})(z{P}_{2})\mathrm{...}(z{P}_{n})},$$
where Z represents the zeros vector, P the poles vector, and K the gain. The number of poles must be greater than or equal to the number of zeros (n ≥ m). If the poles and zeros are complex, they must be complex conjugate pairs.
The block displays the transfer function depending on how the parameters are specified. See ZeroPole for more information.
For a singleoutput system, the input and the output of the block are scalar timedomain signals. To model this system:
Enter a vector for the zeros of the transfer function in the Zeros field.
Enter a vector for the poles of the transfer function in the Poles field.
Enter a 1by1 vector for the gain of the transfer function in the Gain field.
For a multipleoutput system, the block input is a scalar and the output is a vector, where each element is an output of the system. To model this system:
Enter a matrix of zeros in the Zeros field.
Each column of this matrix contains the zeros of a transfer function that relates the system input to one of the outputs.
Enter a vector for the poles common to all transfer functions of the system in the Poles field.
Enter a vector of gains in the Gain field.
Each element is the gain of the corresponding transfer function in Zeros.
Each element of the output vector corresponds to a column in Zeros.
Data Types 

Direct Feedthrough 

Multidimensional Signals 

VariableSize Signals 

ZeroCrossing Detection 
