code: def theoretical_coherence(
      mic_positions: npt.NDArray,
      sample_rate: float,
      field: str = "spherical",
      fft_length: int = 512,
      sound_velocity: float = SOUND_VELOCITY,
  ) -> npt.NDArray:
      """Calculate a theoretical coherence matrix for given mic positions and field type.
  
      Args:
          mic_positions: 3D Cartesian coordinates of microphone positions, shape (num_mics, 3)
          field: string denoting the type of the soundfield
          sample_rate: sampling rate of the input signal in Hz
          fft_length: length of the fft in samples
          sound_velocity: speed of sound in m/s
  
      Returns:
          Calculated coherence with shape (num_subbands, num_mics, num_mics)
      """
      assert (
          mic_positions.shape[1] == 3
      ), "Expecting 3D microphone positions"
      num_mics = mic_positions.shape[0]
  
      if num_mics < 2:
          raise ValueError(
              f"Expecting at least 2 microphones, received {num_mics}"
          )
  
      num_subbands = fft_length // 2 + 1
      angular_freq = (
          2
          * np.pi
          * sample_rate
          * np.arange(0, num_subbands)
          / fft_length
      )
      desired_coherence = np.zeros((num_subbands, num_mics, num_mics))
  
      mic_distance = squareform(pdist(mic_positions))
  
      for p in range(num_mics):
          desired_coherence[:, p, p] = 1.0
          for q in range(p + 1, num_mics):
              dist_pq = mic_distance[p, q]
              if field == "spherical":
                  desired_coherence[:, p, q] = sinc_unnormalized(
                      angular_freq * dist_pq / sound_velocity
                  )
              else:
                  raise ValueError(f"Unknown noise field {field}.")
              # symmetry
              desired_coherence[:, q, p] = desired_coherence[:, p, q]
  
      return desired_coherence
  
imports: import math
  from typing import Iterable, Optional, Union
  import librosa
  import numpy
  import numpy.typing
  import scipy
  import soundfile
  import torch
  from scipy.spatial.distance import pdist, squareform
  from nemo.utils import logging
label_desc: Use image node_id 4 for calling a global function with example usage: theoretical_coherence(mic_positions, sample_rate, field, fft_length, sound_velocity) and returns: desired_coherence