code: def simple_auc(spectrum, f_ppm, center=3.00, bandwidth=0.30):
     
     range = np.max(f_ppm)-np.min(f_ppm)
     dx=float(range)/float(len(f_ppm))
     
     lb = np.floor((np.max(f_ppm)-float(center)+float(bandwidth)/2)/dx)
     ub = np.ceil((np.max(f_ppm)-float(center)-float(bandwidth)/2)/dx)
  
     auc = trapz(spectrum[ub:lb].real, dx=dx)
  
     return auc, ub, lb
docs: Calculates area under the curve (no fitting)
  
     Parameters
     ----------
     spectrum : array of shape (n_transients, n_points)
        Typically the difference of the on/off spectra in each transient.
  
     center, bandwidth : float
        Determine the limits for the part of the spectrum for which we want
        to calculate the AUC.
        e.g. if center = 3.0, bandwidth = 0.3, lower and upper bounds will be
        2.85 and 3.15 respectively (center +/- bandwidth/2).
  
     Notes
     -----
     Default center and bandwidth are 3.0 and 0.3ppm respectively
      because of Sanacora 1999 pg 1045:
     "The GABA signal was integrated over a 0.30-ppm bandwidth at 3.00ppm"
  
     Ref: Sanacora, G., Mason, G. F., Rothman, D. L., Behar, K. L., Hyder, F.,
     Petroff, O. A., ... & Krystal, J. H. (1999). Reduced cortical
     {gamma}-aminobutyric acid levels in depressed patients determined by proton
     magnetic resonance spectroscopy. Archives of general psychiatry, 56(11),
     1043.