IF (intermediate frequency) sampling is a method of sampling the received radar waveform out of the IF channel directly, without mixing to baseband, using a single A/D converter. The sampling rate needed is a multiple of the bandwidth of the IF filter, of the order of 3 times the -3 dB bandwidth. IF filter skirt attenuation limits aliasing effects and permits apparent undersampling of the IF frequency. Stretch processing is the method of matching the radar's LO frequency ramp rate (linear FM) to the transmit waveform's `chirp', in order to limit the IF bandwidth requirement to a value much less than the RF bandwidth and thus permit a lower rate of sampling. The combination of IF sampling and stretch processing is advantageous because A/D samplers are now able to operate at adequately short sample- and-hold aperture times, for use at IF frequencies, with a good number of bits resolution, and stretch processing can use narrow IF bandwidths. Therefore, high range resolution can be achieved at a lower cost than with quadrature channels at baseband and dual A/D's. Added benefits are the elimination of I-Q imbalance effects, A/D DC offset effects, and the need for calibration of these effects. Some A/D saturation can also be tolerated. A Fast Fourier Transform of the real sample data set is easily converted to an inphase and quadrature output data set for further operations. The paper goes into the equations and methodology of such a radar system and delineates the hardware differences between the baseband approach and the IF sampling approach.