code: def test_impulse_response():
      if not numpy:
          skip("NumPy is required for this test")
  
      def impulse_res_tester(sys, expected_value):
          x, y = _to_tuple(
              *impulse_response_numerical_data(
                  sys, adaptive=False, n=10
              )
          )
          x_check = check_point_accuracy(x, expected_value[0])
          y_check = check_point_accuracy(y, expected_value[1])
          return x_check and y_check
  
      exp1 = (
          (
              0.0,
              1.1111111111111112,
              2.2222222222222223,
              3.3333333333333335,
              4.444444444444445,
              5.555555555555555,
              6.666666666666667,
              7.777777777777779,
              8.88888888888889,
              10.0,
          ),
          (
              0.0,
              0.544019738507865,
              0.01993849743234938,
              -0.31140243360893216,
              -0.022852779906491996,
              0.1778306498155759,
              0.01962941084328499,
              -0.1013115194573652,
              -0.014975541213105696,
              0.0575789724730714,
          ),
      )
      exp2 = (
          (
              0.0,
              1.1111111111111112,
              2.2222222222222223,
              3.3333333333333335,
              4.444444444444445,
              5.555555555555555,
              6.666666666666667,
              7.777777777777779,
              8.88888888888889,
              10.0,
          ),
          (
              0.1666666675,
              0.08389223412935855,
              0.02338051973475047,
              -0.014966807776379383,
              -0.034645954223054234,
              -0.040560075735512804,
              -0.037658628907103885,
              -0.030149507719590022,
              -0.021162090730736834,
              -0.012721292737437523,
          ),
      )
      exp3 = (
          (
              0.0,
              1.1111111111111112,
              2.2222222222222223,
              3.3333333333333335,
              4.444444444444445,
              5.555555555555555,
              6.666666666666667,
              7.777777777777779,
              8.88888888888889,
              10.0,
          ),
          (
              4.369893391586999e-09,
              1.1750333000630964,
              3.2922404058312473,
              9.432290008148343,
              28.37098083007151,
              86.18577464367974,
              261.90356653762115,
              795.6538758627842,
              2416.9920942096983,
              7342.159505206647,
          ),
      )
      exp4 = (
          (
              0.0,
              1.1111111111111112,
              2.2222222222222223,
              3.3333333333333335,
              4.444444444444445,
              5.555555555555555,
              6.666666666666667,
              7.777777777777779,
              8.88888888888889,
              10.0,
          ),
          (
              0.0,
              6.17283950617284,
              24.69135802469136,
              55.555555555555564,
              98.76543209876544,
              154.320987654321,
              222.22222222222226,
              302.46913580246917,
              395.0617283950618,
              500.0,
          ),
      )
      exp5 = (
          (
              0.0,
              1.1111111111111112,
              2.2222222222222223,
              3.3333333333333335,
              4.444444444444445,
              5.555555555555555,
              6.666666666666667,
              7.777777777777779,
              8.88888888888889,
              10.0,
          ),
          (
              0.0,
              -0.10455606138085417,
              0.06757671513476461,
              -0.03234567568833768,
              0.013582514927757873,
              -0.005273419510705473,
              0.0019364083003354075,
              -0.000680070134067832,
              0.00022969845960406913,
              -7.476094359583917e-05,
          ),
      )
      exp6 = (
          (
              0.0,
              1.1111111111111112,
              2.2222222222222223,
              3.3333333333333335,
              4.444444444444445,
              5.555555555555555,
              6.666666666666667,
              7.777777777777779,
              8.88888888888889,
              10.0,
          ),
          (
              -6.016699583000218e-09,
              0.35039802056107394,
              3.3728423827689884,
              12.119846079276684,
              25.86101014293389,
              29.352480635282088,
              -30.49475907497664,
              -273.8717189554019,
              -863.2381702029659,
              -1747.0262164682233,
          ),
      )
      exp7 = (
          (
              0.0,
              1.1111111111111112,
              2.2222222222222223,
              3.3333333333333335,
              4.444444444444445,
              5.555555555555555,
              6.666666666666667,
              7.777777777777779,
              8.88888888888889,
              10.0,
          ),
          (
              0.0,
              18.934638095560974,
              5346.93244680907,
              1384609.8718249386,
              358161126.65801865,
              92645770015.70108,
              23964739753087.42,
              6198974342083139.0,
              1.603492601616059e18,
              4.147764422869658e20,
          ),
      )
  
      assert impulse_res_tester(tf1, exp1)
      assert impulse_res_tester(tf2, exp2)
      assert impulse_res_tester(tf3, exp3)
      assert impulse_res_tester(tf4, exp4)
      assert impulse_res_tester(tf5, exp5)
      assert impulse_res_tester(tf7, exp6)
      assert impulse_res_tester(ser1, exp7)
  
imports: from math import isclose
  from sympy.core.numbers import I
  from sympy.core.symbol import Dummy
  from sympy.functions.elementary.complexes import Abs, arg
  from sympy.functions.elementary.exponential import log
  from sympy.abc import s, p, a
  from sympy.external import import_module
  from sympy.physics.control.control_plots import pole_zero_numerical_data, pole_zero_plot, step_response_numerical_data, step_response_plot, impulse_response_numerical_data, impulse_response_plot, ramp_response_numerical_data, ramp_response_plot, bode_magnitude_numerical_data, bode_phase_numerical_data, bode_plot
  from sympy.physics.control.lti import TransferFunction, Series, Parallel, TransferFunctionMatrix
  from sympy.testing.pytest import raises, skip
label_desc: Use image node_id 8 for calling a global function with example usage: test_impulse_response() and returns: unknown