efficient spectrum/fft analysis of sparse signals (found in radar applications) consider the classic scenario of identifying a radar frequency. You typically have a very short pulse of very high RF frequency. For example, a 50ns pulse repeating itself every 1MHz or so (PRF 1MHz and Pulse Repitition Interval 1us) and let's say there are 50 such pulses in each (radar) interrogation so that each set of coherent pulses takes 50us. 

The RF frequency is generally in Gigahertz but let's assume it has been downconverted to lie somewhere between 200MHz to 400MHz. Now you want to analyze this signal after subsampling it at a frequency of 100MHz. The straightforward approach would be to sample the whole 50 us worth of data but in reality the only time is signal is on during the 50us period is 50 times 50 ns which is just 2.5 us. The rest of the signal is just zeros. My question therefore is:


is there a 'smart' way of getting rid of this apparently useless information and hence be able to do a much shorter fft?
is it possible to throw away long strings of zeros in between active pulses, stick the pulses together and perform fft? would that cause any sort of distortion in the spectrum?
One solution for this kind of problem is called an Instantaneous Frequency Measurement (IFM) Receiver. The pulses are located with an envelope detector and a threshold. The average phase change per sample is computed across each pulse; this is proportional to frequency of the pulse.