MTIs. If we say, arbitrarily, that the MTI is blind when the gain drops below -5 dB, we can say that the 2-pulse MTI is blind 27% of the time and the 3- and 4-pulse MTIs are blind 40% and 48% of the time. We would like to improve this situation. A method of doing this is to use staggered PRIs. That is, we use waveforms in which the spacing between pulses changes on a pulse-to-pulse basis. Through this approach we up” “break the orderly structure of the MTI frequency response and in” the nulls. We also “fill reduce the peaks in the frequency response. The net effect is to provide an MTI frequency response that doesn’t have deep nulls and large peaks but, rather, a somewhat constant level. The response still has the null at zero frequency and thus still provides clutter rejection. Figure 2-13 Percent of Time MTI Gain Above Specified Levels – To illustrate how to work with staggered waveforms we consider a 3-pulse MTI and a waveform that alternates between two PRIs of and . A sketch of the waveform is shown in This type of waveform is termed a two-position stagger because it Figure 2-14. uses two PRIs. An n-position stagger would use n PRIs, some of which could be the same. Figure 2-14 Two-Position Stagger Waveform – To determine the frequency response of an MTI with a staggered waveform we work in the continuous time domain and sampling by using impulse functions. Thus, the impulse response of a 3-pulse MTI with binomial coefficients and the waveform above is: . (2-114) If we adjust the time origin so that it is centered on the middle we get . (2-115) This will make some of the math to come a little easier. To find for this filter we find the Fourier transform of and take its magnitude squared. That is, (2-116)
MTIs. If we say, arbitrarily, that the MTI is blind when the gain drops below -5 dB, we can say that the 2-pulse MTI is blind 27% of the time and the 3- and 4-pulse MTIs are blind 40% and 48% of the time. We would like to improve this situation. A method of doing this is to use staggered PRIs. That is, we use waveforms in which the spacing between pulses changes on a pulse-to-pulse basis. Through this approach we “break up” the orderly structure of the MTI frequency response and “fill in” the nulls. We also reduce the peaks in the frequency response. The net effect is to provide an MTI frequency response that doesn’t have deep nulls and large peaks but, rather, a somewhat constant level. The response still has the null at zero frequency and thus still provides clutter rejection. Figure 2-13 – Percent of Time MTI Gain Above Specified Levels To illustrate how to work with staggered waveforms we consider a 3-pulse MTI and a waveform that alternates between two PRIs of and . A sketch of the waveform is shown in Figure 2-14. This type of waveform is termed a two-position stagger because it uses two PRIs. An n-position stagger would use n PRIs, some of which could be the same. Figure 2-14 – Two-Position Stagger Waveform To determine the frequency response of an MTI with a staggered waveform we work in the continuous time domain and sampling by using impulse functions. Thus, the impulse response of a 3-pulse MTI with binomial coefficients and the waveform above is: . (2-114) If we adjust the time origin so that it is centered on the middle we get . (2-115) This will make some of the math to come a little easier. To find for this filter we find the Fourier transform of and take its magnitude squared. That is, (2-116)
SigProc2012.docx