class_docstr: Implementation of the imperceptible attack against a speech recognition model.
  
  | Paper link: http://proceedings.mlr.press/v97/qin19a.html
docstr: Return batch of stabilized masking thresholds and PSD maxima.
  
  :param x: An array with the original inputs to be attacked.
  :return: Tuple consisting of stabilized masking thresholds and PSD maxima.
code: def _stabilized_threshold_and_psd_maximum(
      self, x: np.ndarray
  ) -> Tuple[np.ndarray, np.ndarray]:
      """
      Return batch of stabilized masking thresholds and PSD maxima.
  
      :param x: An array with the original inputs to be attacked.
      :return: Tuple consisting of stabilized masking thresholds and PSD maxima.
      """
      masking_threshold = []
      psd_maximum = []
      x_padded, _ = pad_sequence_input(x)
  
      for x_i in x_padded:
          m_t, p_m = self.masker.calculate_threshold_and_psd_maximum(
              x_i
          )
          masking_threshold.append(m_t)
          psd_maximum.append(p_m)
      # stabilize imperceptible loss by canceling out the "10*log" term in power spectral density maximum and
      # masking threshold
      masking_threshold_stabilized = 10 ** (
          np.array(masking_threshold) * 0.1
      )
      psd_maximum_stabilized = 10 ** (np.array(psd_maximum) * 0.1)
      return masking_threshold_stabilized, psd_maximum_stabilized
  
imports: from __future__ import absolute_import, division, print_function, unicode_literals
  import logging
  from typing import TYPE_CHECKING, Optional, Tuple, Union
  import numpy
  import scipy.signal
  from art.attacks.attack import EvasionAttack
  from art.estimators.estimator import BaseEstimator, LossGradientsMixin, NeuralNetworkMixin
  from art.estimators.pytorch import PyTorchEstimator
  from art.estimators.speech_recognition.speech_recognizer import SpeechRecognizerMixin
  from art.estimators.tensorflow import TensorFlowV2Estimator
  from art.utils import pad_sequence_input
label_desc: Use image node_id 6 for calling the ImperceptibleASR obj's underlying member method code with example usage: obj._stabilized_threshold_and_psd_maximum(x) and returns: masking_threshold_stabilized,  psd_maximum_stabilized