k u03b4 i 2 u2061 k u00b7 u03bc 1 u2061 k u03b4 i 2 u2061 k u03b4 i 2 u2061 k eq u2062 5 d k has a value with tendency toward the group with smaller variance the error er k between the clusters for each sub band k are er i u2061 k u2211 l 1 n i u2062 sgn u2061 u03bc i u2061 k gt d u2061 k u22c0 e i u2061 l lt d u2061 k u2026 u2062 u2062 u2026 sgn u2061 u03bc i u2061 k lt d u2061 k u22c0 e i u2061 l gt d u2061 k eq u2062 6 er u2061 k u2211 i 1 2 u2062 er i u2061 k eq u2062 7 among the selected bands with the same minimum errors the optimum one is selected by using classic scattering formula for each selected frequency band k as the optimum frequency band is then the band which results in the largest s k instead of using s k parameter one can take advantage of statistical distribution of frequency band energies with the least errors the determined arash bands also provides the means for implementation of a smart stethoscope which could be used for automated screening of patients such as children for congenital heart diseases possibly via means using internet.