code: def _fft_conv_center(noncentered, persistence_of_volatility):
      """Transform from noncentered to centered parameterization.
  
      Returns a centered version of `noncentered` such that
      `centered[0] == noncentered[0] / tf.sqrt(1 - persistence_of_volatility**2)`
      and for i > 0
      `centered[i] == noncentered[i] + persistence_of_volatility *
      noncentered[i-1]`.
  
      Rather than implement the recursion directly (which involves expensive
      sequential computation), this function implements it using FFT-based
      convolution.
  
      Args:
        noncentered: A (possibly batched) series of independent normal samples. The
          last dimension is taken to represent time.
        persistence_of_volatility: Scalar between -1 and 1 indicating how strong the
          dependence between time steps should be.
  
      Returns:
        centered: The centered time series.
      """
      noncentered = tf.convert_to_tensor(noncentered)
      persistence_of_volatility = tf.convert_to_tensor(
          persistence_of_volatility
      )
      persistence_of_volatility = persistence_of_volatility[
          ..., tf.newaxis
      ]
      last_dim = int(tuple(noncentered.shape)[-1])
  
      kernel = tf.concat(
          [
              tf.ones_like(persistence_of_volatility),
              persistence_of_volatility
              ** tf.range(1, last_dim, dtype=tf.float32),
          ],
          -1,
      )
      centered_at_0 = tf.concat(
          [
              noncentered[..., :1]
              / tf.sqrt(1 - persistence_of_volatility**2),
              noncentered[..., 1:],
          ],
          -1,
      )
      return _fft_conv(centered_at_0, kernel)[..., :last_dim]
  
imports: import collections
  import tensorflow.compat.v2
  import tensorflow_probability
  from tensorflow_probability.python.internal import distribution_util
  from tensorflow_probability.python.internal import prefer_static
  from inference_gym.internal import data
  from inference_gym.targets import bayesian_model
  from inference_gym.targets import model
  from inference_gym.targets.ground_truth import stochastic_volatility_log_sp500
  from inference_gym.targets.ground_truth import stochastic_volatility_log_sp500_small
  from inference_gym.targets.ground_truth import stochastic_volatility_sp500
  from inference_gym.targets.ground_truth import stochastic_volatility_sp500_small
label_desc: Use image node_id 4 for calling a global function with example usage: _fft_conv_center(noncentered, persistence_of_volatility) and returns: _fft_conv