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# scipy.signal.impulse2

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

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

  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`, `integrate.odeint`

  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

  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)

  (Source code)