Matched Filtration of LFM Signals with Non-Zero Initial Frequency

This paper presents the results of the research considering the influence of the initial frequency on linear frequency modulation signal compression. The signal compression has been performed using the digital matched filtration in the time domain. The ratio of peak to side lobe ratio with the width of the main lobe equaling one sampling period is the measure of the quality of compression. In general, a lower value of peak to side lobe ratio is obtained for linear frequency modulation signals with a non-zero initial frequency than with a zero initial frequency. The peak to side lobe ratio is systematically decreasing with the increase of the initial frequency f_1. The existing methods of band signals sampling, where the spectrum of the signals is transferred by means of the carrier signal $f_0$ of a significantly higher frequency than the band B ($f_0$ ≫ B) may be effectively used for sampling signals considered in this study, which do not have a carrier. As a result, for the linear frequency modulation signals with a non-zero initial frequency $f_1$ = nB and a final frequency $f_2$ = (n + 1) B, n = 1, 2, ..., the same peak to side lobe ratio values will be obtained as for linear frequency modulation signals with a zero initial frequency and the identical band and time duration. The results of this research could be implemented in sonar and radiolocation techniques and medicine.