# scipy.signal.impulse2

scipy.signal.impulse2(system, X0=None, T=None, N=None, **kwargs)

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

  Deprecated since version 1.11.0: Function `impulse2` is deprecated in favor of the faster `impulse` function. `impulse2` will be removed in SciPy 1.13.

  Parameters:
    system an 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)

    X0 1-D array_like, optional

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

    T 1-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.

    N int, optional

      Number of time points to compute. Default: 100.

    kwargs various 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:
    T ndarray

      The time values for the output.

    yout ndarray

      The output response of the system.

  See also

  `impulse`, `lsim2`, `scipy.integrate.odeint`

  Notes

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

  As `impulse2` is now deprecated, users are advised to switch to the faster and more accurate `impulse` function. Keyword arguments for `scipy.integrate.odeint` are not supported in `impulse`, but not needed in general.

  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)