code: def istft(
      Zxx: Array,
      fs: ArrayLike = 1.0,
      window: str = "hann",
      nperseg: int | None = None,
      noverlap: int | None = None,
      nfft: int | None = None,
      input_onesided: bool = True,
      boundary: bool = True,
      time_axis: int = -1,
      freq_axis: int = -2,
  ) -> tuple[Array, Array]:
      # Input validation
      check_arraylike("istft", Zxx)
      if Zxx.ndim < 2:
          raise ValueError("Input stft must be at least 2d!")
      freq_axis = canonicalize_axis(freq_axis, Zxx.ndim)
      time_axis = canonicalize_axis(time_axis, Zxx.ndim)
      if freq_axis == time_axis:
          raise ValueError(
              "Must specify differing time and frequency axes!"
          )
  
      Zxx = jnp.asarray(
          Zxx,
          dtype=jax.dtypes.canonicalize_dtype(
              np.result_type(Zxx, np.complex64)
          ),
      )
  
      n_default = (
          2 * (Zxx.shape[freq_axis] - 1)
          if input_onesided
          else Zxx.shape[freq_axis]
      )
  
      nperseg_int = jax.core.concrete_or_error(
          int, nperseg or n_default, "nperseg: segment length of STFT"
      )
      if nperseg_int < 1:
          raise ValueError("nperseg must be a positive integer")
  
      nfft_int: int = 0
      if nfft is None:
          nfft_int = n_default
          if input_onesided and nperseg_int == n_default + 1:
              nfft_int += 1  # Odd nperseg, no FFT padding
      else:
          nfft_int = jax.core.concrete_or_error(
              int, nfft, "nfft of STFT"
          )
      if nfft_int < nperseg_int:
          raise ValueError(
              f"FFT length ({nfft_int}) must be longer than nperseg ({nperseg_int})."
          )
  
      noverlap_int = jax.core.concrete_or_error(
          int, noverlap or nperseg_int // 2, "noverlap of STFT"
      )
      if noverlap_int >= nperseg_int:
          raise ValueError("noverlap must be less than nperseg.")
      nstep = nperseg_int - noverlap_int
  
      # Rearrange axes if necessary
      if time_axis != Zxx.ndim - 1 or freq_axis != Zxx.ndim - 2:
          outer_idxs = tuple(
              idx
              for idx in range(Zxx.ndim)
              if idx not in {time_axis, freq_axis}
          )
          Zxx = jnp.transpose(Zxx, outer_idxs + (freq_axis, time_axis))
  
      # Perform IFFT
      ifunc = (
          jax.numpy.fft.irfft if input_onesided else jax.numpy.fft.ifft
      )
      # xsubs: [..., T, N], N is the number of frames, T is the frame length.
      xsubs = ifunc(Zxx, axis=-2, n=nfft)[..., :nperseg_int, :]
  
      # Get window as array
      if isinstance(window, (str, tuple)):
          win = osp_signal.get_window(window, nperseg_int)
          win = jnp.asarray(win, dtype=xsubs.dtype)
      else:
          win = jnp.asarray(window)
          if len(win.shape) != 1:
              raise ValueError("window must be 1-D")
          if win.shape[0] != nperseg_int:
              raise ValueError(
                  f"window must have length of {nperseg_int}"
              )
      xsubs *= win.sum()  # This takes care of the 'spectrum' scaling
  
      # make win broadcastable over xsubs
      win = lax.expand_dims(win, (*range(xsubs.ndim - 2), -1))
      x = _overlap_and_add((xsubs * win).swapaxes(-2, -1), nstep)
      win_squared = jnp.repeat((win * win), xsubs.shape[-1], axis=-1)
      norm = _overlap_and_add(win_squared.swapaxes(-2, -1), nstep)
  
      # Remove extension points
      if boundary:
          x = x[..., nperseg_int // 2 : -(nperseg_int // 2)]
          norm = norm[..., nperseg_int // 2 : -(nperseg_int // 2)]
      x /= jnp.where(norm > 1e-10, norm, 1.0)
  
      # Put axes back
      if x.ndim > 1:
          if time_axis != Zxx.ndim - 1:
              if freq_axis < time_axis:
                  time_axis -= 1
              x = jnp.moveaxis(x, -1, time_axis)
  
      time = jnp.arange(x.shape[0], dtype=np.finfo(x.dtype).dtype) / fs
      return time, x
  
imports: from __future__ import annotations
  from collections.abc import Sequence
  from functools import partial
  import math
  import operator
  from typing import Callable
  import warnings
  import numpy
  import scipy.signal
  from scipy.fft import next_fast_len
  import jax
  import jax.numpy.fft
  import jax.numpy
  from jax import lax
  from jax._src.api_util import _ensure_index_tuple
  from jax._src import dtypes
  from jax._src.lax.lax import PrecisionLike
  from jax._src.numpy import linalg
  from jax._src.numpy.util import check_arraylike, _wraps, promote_dtypes_inexact, promote_dtypes_complex
  from jax._src.third_party.scipy import signal_helper
  from jax._src.typing import Array, ArrayLike
  from jax._src.util import canonicalize_axis, tuple_delete, tuple_insert
label_desc: Use image node_id 16 for calling a global function with example usage: istft(Zxx, fs, window, nperseg, noverlap, nfft, input_onesided, boundary, time_axis, freq_axis) and returns: time,  x