One could think that the using of long probing signals with small magnitude and phase modulation with receiver's signal compression by means of a matched filter (MF) for maximization both of SNR and resolving power in the time domain (as is the case in ordinary radar and sonar systems) would be the simplest way for settling the problem. However, MF-method is not realizable when probing dispersive structures with large attenuation coefficient (DSLAC) because a law of signal distortion by structure remains unknown.

The generalized matched filtering method (GMFM) allows to ensure the deepest probing of a DSLAC with arbitrary law of signal distortion by the structure. The GMF-methodology is based on probing a DSLAC with signals that represent the DSLAC's eigenfunctions whose shapes are not distorted by the DSLAC with subsequent digital integral transform to perform the synthesis of resulting reflectogram in the time domain.

From the point of view of attainable technical characteristics, implementation of GMFM ensures potential possibility for qualitative development of methods for local ultrasonic introscopy. Specifically, unlike the conventional method of pulse probing, GMFM allows:

1. to increase the energy of equivalent probing signal in up to 108 times given specific radiation power;

2. to increase sensibility of measurements in 10-100 times on the basis of optimum filtering method of signals with known shape;

3. to increase accuracy of measurements in 10-100 times by using of many-digit A/D converters (with no less than 12 digits) in quasistatic measuring mode;

4. to decrease the likelihood of arising of artifacts in a reflectogram by means of eliminating the necessity of using the time automatic amplification system.

In its essence, the GMFM pertains to the field of "Computer Synthesis" methods. Its implementation time is comparable to that of signal reconstruction in the Computer Tomography and depends on relation between probing depth and requirements on resolving power in the time domain.