code: def __reassign_frequencies(
      y: np.ndarray,
      sr: float = 22050,
      S: Optional[np.ndarray] = None,
      n_fft: int = 2048,
      hop_length: Optional[int] = None,
      win_length: Optional[int] = None,
      window: _WindowSpec = "hann",
      center: bool = True,
      dtype: Optional[DTypeLike] = None,
      pad_mode: _PadModeSTFT = "constant",
  ) -> Tuple[np.ndarray, np.ndarray]:
      """Instantaneous frequencies based on a spectrogram representation.
  
      The reassignment vector is calculated using equation 5.20 in Flandrin,
      Auger, & Chassande-Mottin 2002::
  
          omega_reassigned = omega - np.imag(S_dh/S_h)
  
      where ``S_h`` is the complex STFT calculated using the original window, and
      ``S_dh`` is the complex STFT calculated using the derivative of the original
      window.
  
      See `reassigned_spectrogram` for references.
  
      It is recommended to use ``pad_mode="wrap"`` or else ``center=False``, rather
      than the defaults. Frequency reassignment assumes that the energy in each
      FFT bin is associated with exactly one signal component. Reflection padding
      at the edges of the signal may invalidate the reassigned estimates in the
      boundary frames.
  
      Parameters
      ----------
      y : np.ndarray [shape=(..., n,)], real-valued
          audio time series. Multi-channel is supported.
  
      sr : number > 0 [scalar]
          sampling rate of ``y``
  
      S : np.ndarray [shape=(..., d, t)] or None
          (optional) complex STFT calculated using the other arguments provided
          to `__reassign_frequencies`
  
      n_fft : int > 0 [scalar]
          FFT window size. Defaults to 2048.
  
      hop_length : int > 0 [scalar]
          hop length, number samples between subsequent frames.
          If not supplied, defaults to ``win_length // 4``.
  
      win_length : int > 0, <= n_fft
          Window length. Defaults to ``n_fft``.
          See ``stft`` for details.
  
      window : string, tuple, number, function, or np.ndarray [shape=(n_fft,)]
          - a window specification (string, tuple, number);
            see `scipy.signal.get_window`
          - a window function, such as `scipy.signal.windows.hann`
          - a user-specified window vector of length ``n_fft``
  
          See `stft` for details.
  
          .. see also:: `filters.get_window`
  
      center : boolean
          - If ``True``, the signal ``y`` is padded so that frame
            ``S[:, t]`` is centered at ``y[t * hop_length]``.
          - If ``False``, then ``S[:, t]`` begins at ``y[t * hop_length]``.
  
      dtype : numeric type
          Complex numeric type for ``S``. Default is inferred to match
          the numerical precision of the input signal.
  
      pad_mode : string
          If ``center=True``, the padding mode to use at the edges of the signal.
          By default, STFT uses zero padding.
  
      Returns
      -------
      freqs : np.ndarray [shape=(..., 1 + n_fft/2, t), dtype=real]
          Instantaneous frequencies:
          ``freqs[f, t]`` is the frequency for bin ``f``, frame ``t``.
      S : np.ndarray [shape=(..., 1 + n_fft/2, t), dtype=complex]
          Short-time Fourier transform
  
      Warns
      -----
      RuntimeWarning
          Frequencies with zero support will produce a divide-by-zero warning and
          will be returned as `np.nan`.
  
      See Also
      --------
      stft : Short-time Fourier Transform
      reassigned_spectrogram : Time-frequency reassigned spectrogram
  
      Examples
      --------
      >>> y, sr = librosa.load(librosa.ex('trumpet'))
      >>> frequencies, S = librosa.core.spectrum.__reassign_frequencies(y, sr=sr)
      >>> frequencies
      array([[0.000e+00, 0.000e+00, ..., 0.000e+00, 0.000e+00],
             [3.628e+00, 4.698e+00, ..., 1.239e+01, 1.072e+01],
             ...,
             [1.101e+04, 1.102e+04, ..., 1.105e+04, 1.102e+04],
             [1.102e+04, 1.102e+04, ..., 1.102e+04, 1.102e+04]])
      """
      # retrieve window samples if needed so that the window derivative can be
      # calculated
      if win_length is None:
          win_length = n_fft
  
      window = get_window(window, win_length, fftbins=True)
      window = util.pad_center(window, size=n_fft)
  
      if S is None:
          if dtype is None:
              dtype = util.dtype_r2c(y.dtype)
  
          S_h = stft(
              y=y,
              n_fft=n_fft,
              hop_length=hop_length,
              window=window,
              center=center,
              dtype=dtype,
              pad_mode=pad_mode,
          )
  
      else:
          if dtype is None:
              dtype = S.dtype
  
          S_h = S
  
      # cyclic gradient to correctly handle edges of a periodic window
      window_derivative = util.cyclic_gradient(window)
  
      S_dh = stft(
          y=y,
          n_fft=n_fft,
          hop_length=hop_length,
          window=window_derivative,
          center=center,
          dtype=dtype,
          pad_mode=pad_mode,
      )
  
      # equation 5.20 of Flandrin, Auger, & Chassande-Mottin 2002
      # the sign of the correction is reversed in some papers - see Plante,
      # Meyer, & Ainsworth 1998 pp. 283-284
      with np.errstate(invalid="ignore"):
          # We can ignore divide-by-zero here because NaN is an acceptable correction value
          correction = -np.imag(S_dh / S_h)
  
      freqs = convert.fft_frequencies(sr=sr, n_fft=n_fft)
      freqs = util.expand_to(
          freqs, ndim=correction.ndim, axes=-2
      ) + correction * (0.5 * sr / np.pi)
  
      return freqs, S_h
  
imports: from __future__ import annotations
  import warnings
  import numpy
  import scipy
  import scipy.ndimage
  import scipy.signal
  import scipy.interpolate
  from numba import jit
  from .None import convert
  from .fft import get_fftlib
  from .audio import resample
  from .._cache import cache
  from ..None import util
  from ..util.exceptions import ParameterError
  from ..filters import get_window, semitone_filterbank
  from ..filters import window_sumsquare
  from numpy.typing import DTypeLike
  from typing import Any, Callable, Optional, Tuple, List, Union, overload
  from typing_extensions import Literal
  from .._typing import _WindowSpec, _PadMode, _PadModeSTFT, _SequenceLike, _ScalarOrSequence, _ComplexLike_co, _FloatLike_co
label_desc: Use image node_id 4 for calling a global function with example usage: __reassign_frequencies(y, sr, S, n_fft, hop_length, win_length, window, center, dtype, pad_mode) and returns: freqs,  S_h