The concept of Time Reversal Acoustics (TRA) provides an elegant possibility of both temporal and spatial concentrating of acoustic energy in highly inhomogeneous media. We explored the possibility of generating acoustical signals with arbitrary waveforms using the TRA Focusing System (TRA FS). A method has been developed to predict TRA focused ultrasound waveforms and spatial distribution by using the measurements of transfer function of transfer function relating the signal at the TRA transmitter to that at the focusing point. The developed approach for TRA-focused signal waveform prediction from the results of direct signal measurements was tested on ten-channel TRA FS based on aluminum resonator with glued piezotransducers. The TRA FS operated in the frequency band of 100-1000 kHz. The formation of ultrasonic signals with various envelopes was demonstrated experimentally. The calculated and experimentally measured waveforms and spatial distributions were practically identical. We formed triangular, rectangular, and amplitude modulated tone burst signals with different modulation frequencies in the focal region. The level of side lobes in the generated signals was much lower than that for standard TRA focusing.