code: def _calc_dual_canonical_window(
      win: np.ndarray, hop: int
  ) -> np.ndarray:
      """Calculate canonical dual window for 1d window `win` and a time step
      of `hop` samples.
  
      A ``ValueError`` is raised, if the inversion fails.
  
      This is a separate function not a method, since it is also used in the
      class method ``ShortTimeFFT.from_dual()``.
      """
      if hop > len(win):
          raise ValueError(
              f"{hop=} is larger than window length of {len(win)}"
              + " => STFT not invertible!"
          )
      if issubclass(win.dtype.type, np.integer):
          raise ValueError(
              "Parameter 'win' cannot be of integer type, but "
              + f"{win.dtype=} => STFT not invertible!"
          )
          # The calculation of `relative_resolution` does not work for ints.
          # Furthermore, `win / DD` casts the integers away, thus an implicit
          # cast is avoided, which can always cause confusion when using 32-Bit
          # floats.
  
      w2 = (
          win.real**2 + win.imag**2
      )  # win*win.conj() does not ensure w2 is real
      DD = w2.copy()
      for k_ in range(hop, len(win), hop):
          DD[k_:] += w2[:-k_]
          DD[:-k_] += w2[k_:]
  
      # check DD > 0:
      relative_resolution = np.finfo(win.dtype).resolution * max(DD)
      if not np.all(DD >= relative_resolution):
          raise ValueError(
              "Short-time Fourier Transform not invertible!"
          )
  
      return win / DD
  
imports: from __future__ import annotations
  from collections.abc import Generator
  from functools import cache, lru_cache, partial
  from typing import Callable, get_args, Literal
  import numpy
  import scipy.fft
  from scipy.signal import detrend
  from scipy.signal.windows import get_window
label_desc: Use image node_id 1 for calling a global function with example usage: _calc_dual_canonical_window(win, hop) and returns: unknown