Principles of Modern Radar - Volume 2 1891121537

62 CHAPTER 2 Advanced Pulse Compression Waveform ModulationsFIGURE 2-25 ASF waveform’scompressedresponse is a digitalsinc function.50−5−10dB−15−20−25−30−35−40−3 −2 −1 0 1 2 3ωThe waveform’s Rayleigh resolution is found by setting the argument of the numeratorin equation (2.115) equal to π and solving for ωδω = 2π N(2.116)where δω is the resolution in terms of digital frequency. To convert the frequency resolutionin equation (2.116) to a range resolution, consider two point targets located at ranges R 1and R 2 and separated in range by δR = |R 2 − R 1 |. The difference in their phase rotationrates is 2π 2δR f . Equating the rate difference to the frequency resolution defined incequation (2.116)2π 2δRcf = 2π Nand solving for the range difference yields the Rayleigh resolutionδR =c2Nf(2.117)(2.118)The range resolution achieved by the SF waveform is inversely proportional to the waveform’scomposite bandwidth Nf . In this case, the Rayleigh resolution is equivalent tothe main lobe’s –4 dB width.2.5.4.2 Discrete Fourier TransformThe DTFT is defined over continuous frequency; however, to realize the compressedresponse in digital hardware requires one to evaluate the DTFT at a finite number offrequencies over the interval [0, 2π). It is common to evaluate the DTFT at equally spacedfrequenciesω k = 2π k Mk = 0,...,(M − 1) (2.119)