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The spectral amplitude damping of Barkhausen noise is determined theoretically and experimentally as a function of distance inside the sample itself. Power spectra for noise amplitude and its time derivative are measured in some steel specimens over a wide frequency range. Some examples of the influence of the sample microstructure on the power spectra are also examined. The results, including spectral damping, suggest that the nature of Barkhausen noise changes continuously from nonrandom to random either with the thickness of the sample (0.1-5 mm) or with increasing magnetizing frequency (10-2-102Hz). This phenomenon as a whole is explained in terms of the clustering of elementary magnetization transitions.