code: def function_1d(x):
      """Estimate the normalized autocorrelation function of a 1-D series
  
      Args:
          x: The series as a 1-D numpy array.
  
      Returns:
          array: The autocorrelation function of the time series.
  
      """
      x = np.atleast_1d(x)
      if len(x.shape) != 1:
          raise ValueError(
              "invalid dimensions for 1D autocorrelation function"
          )
      n = next_pow_two(len(x))
  
      # Compute the FFT and then (from that) the auto-correlation function
      f = np.fft.fft(x - np.mean(x), n=2 * n)
      acf = np.fft.ifft(f * np.conjugate(f))[: len(x)].real
      acf /= acf[0]
      return acf
  
file_path: emcee/src/emcee/autocorr.py
imports: import logging
  import numpy
label_desc: Use image node_id 2 for calling a global function with example usage: function_1d(x) and returns: acf