scipy.signal.dlti

class scipy.signal.dlti(*system, **kwargs)

Discrete-time linear time invariant system base class.

Parameters:

*system: arguments

The dlti class can be instantiated with either 2, 3 or 4 arguments. The following gives the number of arguments and the corresponding discrete-time subclass that is created:

• 2: TransferFunction: (numerator, denominator)

• 3: ZerosPolesGain: (zeros, poles, gain)

• 4: StateSpace: (A, B, C, D)

Each argument can be an array or a sequence.

dt: float, optional

Sampling time [s] of the discrete-time systems. Defaults to True (unspecified sampling time). Must be specified as a keyword argument, for example, dt=0.1.

See also

ZerosPolesGain, StateSpace, TransferFunction, lti

Notes

dlti instances do not exist directly. Instead, dlti creates an instance of one of its subclasses: StateSpace, TransferFunction or ZerosPolesGain.

Changing the value of properties that are not directly part of the current system representation (such as the zeros of a StateSpace system) 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_zpk() before accessing/changing the zeros, poles or gain.

If (numerator, denominator) is passed in for *system, coefficients for both the numerator and denominator should be specified in descending exponent order (e.g., z^2 + 3z + 5 would be represented as [1, 3, 5]).

Added in version 0.18.0.

Examples

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>>> from scipy import signal

>>> signal.dlti(1, 2, 3, 4)
StateSpaceDiscrete(
array([[1]]),
array([[2]]),
array([[3]]),
array([[4]]),
dt: True
)

>>> signal.dlti(1, 2, 3, 4, dt=0.1)
StateSpaceDiscrete(
array([[1]]),
array([[2]]),
array([[3]]),
array([[4]]),
dt: 0.1
)

Construct the transfer function \(H(z) = \frac{5(z - 1)(z - 2)}{(z - 3)(z - 4)}\) with a sampling time of 0.1 seconds:

>>> signal.dlti([1, 2], [3, 4], 5, dt=0.1)
ZerosPolesGainDiscrete(
array([1, 2]),
array([3, 4]),
5,
dt: 0.1
)

Construct the transfer function \(H(z) = \frac{3z + 4}{1z + 2}\) with a sampling time of 0.1 seconds:

>>> signal.dlti([3, 4], [1, 2], dt=0.1)
TransferFunctionDiscrete(
array([3., 4.]),
array([1., 2.]),
dt: 0.1
)

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Attributes:

dt

Return the sampling time of the system.

poles

Poles of the system.

zeros

Zeros of the system.

Methods

bode([w, n])	Calculate Bode magnitude and phase data of a discrete-time system.
freqresp([w, n, whole])	Calculate the frequency response of a discrete-time system.
impulse([x0, t, n])	Return the impulse response of the discrete-time dlti system.
output(u, t[, x0])	Return the response of the discrete-time system to input u.
step([x0, t, n])	Return the step response of the discrete-time dlti system.