Methods for enhancement of data obtained from scanning objects such as body tissue with ultrasonic wideband pulses to detect characteristics of the tissue and to identify the tissue. The methods include performing spectral analysis on selected time portions of signals obtained from ultrasonic scanning to derive spectral data which is representative of the received signal characteristics for spatial samples of a particular region of interest in the body. The characteristic values are selected to correlate with significant characteristics of the material. A display of the selected body region is generated, with the display characteristic for each of the spatial samples being selected in accordance with the derived spectral characteristic values. Examples of the spectral characteristic values include spectral amplitude, spectral slope, and spectral amplitude uncertainty. The spectral characteristic data can be used to derive periodicity data, such as cepstral data or spatial-correlation data, for each of the spatial samples. The spectral characteristic data obtained can be compared to data for tissue having known tissue characteristics to identify the tissue type. Related means for suppressing the display of noise, characterizing tissues using discriminent functions based on spectral data, and estimating scatter sizes are also shown.