Inverse Synthetic Aperture Radar Imaging With MATLAB Algorithms. Caner Ozdemir

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2.19a), its time duration has to be quite small such that it may not be possible to put enough energy on it. A solution to this problem is to use a modulated pulse of sufficient duration such that this modulated waveform provides the required frequency bandwidth for the operation of radar.

Graphs depicts short-duration rectangular pulse in (a) time domain, (b) frequency domain. Graphs depicts short-duration single-frequency pulse in (a) time domain, (b) frequency domain. Graphs depict short-duration Mexican-hat pulse in (a) time domain, (b) frequency domain. Graphs depict of the time-domain pulse waveforms: (a) single-tone pulse, (b) LFM (Chirp) pulse.

      The common waveform is the LFM pulse, also known as the chirp pulse, whose waveform is shown in Figure 2.19b. In practice, this waveform is repeated in every TPR intervals for most common radar applications, especially for localization of targets in the range. TPR is called the pulse repetition interval (PRI) or pulse repetition period. The inverse of this interval gives the pulse repetition frequency (PRF), defined as

      The mathematical expression of the upward chirp signal whose frequency is increasing as time passes along the pulse is given as

      (2.61)equation

      where n is an integer, τ is the pulse width, and K is the chirp rate. The instantaneous frequency of the pulse is fi(t) = fo + Kt. It is also possible to form another LFM pulse by decreasing the frequency along the pulse width as shown below:

      (2.62)equation

      For the downward chirp pulse, the instantaneous frequency is then equal to fi(t) = foKt.

      In radar applications, LFM pulse waveforms are mainly utilized in finding range profiles, and also for synthetic aperture radar (SAR) and ISAR processing as will be discussed in Chapters 3 and 6, respectively.

      2.7.1 Pulse Repetition Frequency

      2.7.2 Maximum Range and Range Ambiguity

      (2.63)equation

Schematic illustration of radar systems use a sequence of modulated pulses.

      (2.64)equation

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