# scipy.signal.impulse2#

scipy.signal.impulse2(system, X0=None, T=None, N=None, **kwargs)[source]#

Impulse response of a single-input, continuous-time linear system.

Parameters:
systeman instance of the LTI class or a tuple of array_like

describing the system. The following gives the number of elements in the tuple and the interpretation:

• 1 (instance of `lti`)

• 2 (num, den)

• 3 (zeros, poles, gain)

• 4 (A, B, C, D)

X01-D array_like, optional

The initial condition of the state vector. Default: 0 (the zero vector).

T1-D array_like, optional

The time steps at which the input is defined and at which the output is desired. If T is not given, the function will generate a set of time samples automatically.

Nint, optional

Number of time points to compute. Default: 100.

kwargsvarious types

Additional keyword arguments are passed on to the function `scipy.signal.lsim2`, which in turn passes them on to `scipy.integrate.odeint`; see the latter’s documentation for information about these arguments.

Returns:
Tndarray

The time values for the output.

youtndarray

The output response of the system.

Notes

The solution is generated by calling `scipy.signal.lsim2`, which uses the differential equation solver `scipy.integrate.odeint`.

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

New in version 0.8.0.

Examples

Compute the impulse response of a second order system with a repeated root: `x''(t) + 2*x'(t) + x(t) = u(t)`

```>>> from scipy import signal
>>> system = ([1.0], [1.0, 2.0, 1.0])
>>> t, y = signal.impulse2(system)
>>> import matplotlib.pyplot as plt
>>> plt.plot(t, y)
```