Linear Time Invariant system class in zeros, poles, gain form.
Represents the system as the continuous- or discrete-time transfer function :math:`H(s)=k \prod_i (s - zi) / \prod_j (s - pj)`, where :math:`k` is the `gain`, :math:`z` are the `zeros` and :math:`p` are the `poles`. `ZerosPolesGain` systems inherit additional functionality from the `lti`, respectively the `dlti` classes, depending on which system representation is used.
Parameters ---------- *system : arguments The `ZerosPolesGain` class can be instantiated with 1 or 3 arguments. The following gives the number of input arguments and their interpretation:
* 1: `lti` or `dlti` system: (`StateSpace`, `TransferFunction` or `ZerosPolesGain`) * 3: array_like: (zeros, poles, gain) dt: float, optional Sampling time s of the discrete-time systems. Defaults to `None` (continuous-time). Must be specified as a keyword argument, for example, ``dt=0.1``.
See Also -------- TransferFunction, StateSpace, lti, dlti zpk2ss, zpk2tf, zpk2sos
Notes ----- Changing the value of properties that are not part of the `ZerosPolesGain` system representation (such as the `A`, `B`, `C`, `D` state-space matrices) is very inefficient and may lead to numerical inaccuracies. It is better to convert to the specific system representation first. For example, call ``sys = sys.to_ss()`` before accessing/changing the A, B, C, D system matrices.
Examples -------- >>> from scipy import signal
Transfer function: H(s) = 5(s - 1)(s - 2) / (s - 3)(s - 4)
>>> signal.ZerosPolesGain(1, 2, 3, 4, 5) ZerosPolesGainContinuous( array(1, 2), array(3, 4), 5, dt: None )
Transfer function: H(z) = 5(z - 1)(z - 2) / (z - 3)(z - 4)
>>> signal.ZerosPolesGain(1, 2, 3, 4, 5, dt=0.1) ZerosPolesGainDiscrete( array(1, 2), array(3, 4), 5, dt: 0.1 )