Читать книгу Inverse Synthetic Aperture Radar Imaging With MATLAB Algorithms - Caner Ozdemir - Страница 69

One of the simplest radar waveforms is the short pulse (or impulse) whose time duration is usually on the order of a few nanoseconds. As calculated in Eq. 2.54, the range resolution of a pulsed radar is equal to

(2.56)

where B is the frequency bandwidth of the pulse. According to the Fourier theory, the frequency bandwidth, B of a pulse is also inversely proportional to its pulse duration as

(2.57)

which means that the range resolution is proportional to its pulse duration as

(2.58)

Therefore, to have a good range resolution, the duration of a pulse has to be as small as possible. Common short pulse waveforms are rectangular pulse, single‐tone pulse, and single wavelet pulse of different forms. In Figure 2.16a, a rectangular pulse‐shape wave is shown, and the spectrum of this signal is plotted in Figure 2.16b. In the frequency domain, a sinc‐type pattern is obtained as expected.

Another common single‐pulse shape is a single sine signal as plotted in Figure 2.17. Since the time‐domain pulse is smoother when compared to the rectangular pulse (see Figure 2.17a), the spectrum widens, and sidelobe levels decrease as expected according to the Fourier theory as depicted in Figure 2.17b.

Another popular short‐duration waveform is called the wavelet signal. Wavelets are much smoother than the sine pulse; therefore, they provide less sidelobes in the frequency domain. In Figure 2.18a, a Mexican‐hat type wavelet whose mathematical function is given below is shown below:

(2.59)

Since this signal is much smoother than the previous short pulse waveforms that we have presented, the frequency extent of this wavelet is extremely broad. Therefore, it provides an ultrawide band (UWB) spectrum as most of the other short‐duration wavelets do as shown in Figure 2.18b.

While these short pulses are good for providing a wide spectrum, they are not practical in terms of providing sufficient energy. This is because of the fact that it is not possible to put great amount of power onto a very small pulse. To circumvent this problem, the pulse is modulated by altering the frequency as time continues to pass. The common practice is to use a chirp waveform to be able to put enough energy onto the pulse, as will be investigated next.