Signals with linear frequency modulation are used in synthetic aperture radar to improve spatial resolution and signal/noise ratio. Acoustic field is proposed in this paper to investigate objects, because it could penetrate them, and propagate inside. When input signal frequency is about resonance frequency, the attenuation is increased, and as a result, the scattered acoustic field is decreased as well. So, a linear frequency modulation signal with constant amplitude is sent to the investigated object, and variable amplitude is reflected, corresponding to the object resonance frequencies. A new method for detection the amplitude modulation of these signals in presence of noise is presented. The method uses the fractional Fourier transform in two steps. In the first step a rotation of signal by the angle=450 is done. The all spectral components outside central band are canceled. After that a new rotation of new function with the same angle is done. The simulated results are presented. The method gives good results of amplitude modulation detection for signals with complex modulation signals having signal - noise ratio in power up to - 5 dB. By knowing the resonance frequencies it is possible to specify the largest 3D object dimension, appreciate the relative values of the other dimensions, and do a rough classification of that object. The presented method could be used for rough classification of buried objects in earth or to early diagnose whether a tumor tissue is or not malignant.