code: def test_impulse_roundtrip(i):
      """Roundtrip for an impulse being at different positions `i`."""
      n = 19
      w, h_n = np.ones(8), 3
      x = np.zeros(n)
      x[i] = 1
  
      SFT = ShortTimeFFT(
          w, hop=h_n, fs=1, scale_to=None, phase_shift=None
      )
      Sx = SFT.stft(x)
      # test slicing the input signal into two parts:
      n_q = SFT.nearest_k_p(n // 2)
      Sx0 = SFT.stft(x[:n_q], padding="zeros")
      Sx1 = SFT.stft(x[n_q:], padding="zeros")
      q0_ub = SFT.upper_border_begin(n_q)[1] - SFT.p_min
      q1_le = SFT.lower_border_end[1] - SFT.p_min
      assert_allclose(Sx0[:, :q0_ub], Sx[:, :q0_ub], err_msg=f"{i=}")
      assert_allclose(
          Sx1[:, q1_le:], Sx[:, q1_le - Sx1.shape[1] :], err_msg=f"{i=}"
      )
  
      Sx01 = np.hstack(
          (
              Sx0[:, :q0_ub],
              Sx0[:, q0_ub:] + Sx1[:, :q1_le],
              Sx1[:, q1_le:],
          )
      )
      assert_allclose(Sx, Sx01, atol=1e-8, err_msg=f"{i=}")
  
      y = SFT.istft(Sx, 0, n)
      assert_allclose(y, x, atol=1e-8, err_msg=f"{i=}")
      y0 = SFT.istft(Sx, 0, n // 2)
      assert_allclose(x[: n // 2], y0, atol=1e-8, err_msg=f"{i=}")
      y1 = SFT.istft(Sx, n // 2, n)
      assert_allclose(x[n // 2 :], y1, atol=1e-8, err_msg=f"{i=}")
  
imports: import math
  from itertools import product
  from typing import cast, get_args, Literal
  import numpy
  import pytest
  from numpy.testing import assert_allclose, assert_equal
  from scipy.fft import fftshift
  from scipy.stats import norm
  from scipy.signal import get_window, welch, stft, istft, spectrogram
  from scipy.signal._short_time_fft import FFT_MODE_TYPE, _calc_dual_canonical_window, ShortTimeFFT, PAD_TYPE
  from scipy.signal.windows import gaussian
label_desc: Use image node_id 20 for calling a global function with example usage: test_impulse_roundtrip(i) without return types