An ultrasonic system with a linear array for characterization of a layered specimen placed in immersion liquid parallel to the aperture of the array is considered. To estimate the longitudinal and transverse wave velocities as well as the thickness and density of the specimen, it is proposed to decompose the spatio-temporal data recorded by the array in a spectrum of plane pulse waves. Based on fitting the developed wave model of the system to the experimental data, it is shown that the relative delays and amplitudes of the spectral responses can be used for the estimation of the velocities and thickness of the layer and its density. The distortions of the plane wave spectrum caused by the spatial discretization of the array data are considered. It is proposed to suppress these distortions using individual interpolating processing of the received pulses separated in the spatio-temporal domain. The developed technique is experimentally verified on a fused quartz plate evaluated with a 17-MHz linear array. The relative reproducibility of the estimation is found to be 0.11% in the longitudinal wave velocity and thickness of the plate, and 0.5% and 5% in the transverse wave velocity and the density, respectively.