Inverse Synthetic Aperture Radar Imaging With MATLAB Algorithms. Caner Ozdemir

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frequency content such as speech and music signals. In these cases, the single‐frequency sinusoidal bases are not considered to be suitable for the detailed analysis of those signals. Therefore, JTF analysis methods were developed to represent these signals both in time and frequency to observe the variation of frequency content as the time progresses.

      There are many tools to map a time domain or frequency‐domain signal onto the JFT plane. Some of the most well‐known JFT tools are short‐time Fourier transform (STFT) (Allen 1977), Wigner–Ville distribution (Nuttall 1988), Choi–Willams distribution (Du and Su 2003), Cohen's class (Cohen 1989), and time‐frequency distribution series (TFDS) (Qian and Chen 1996). Among these, the most appreciated and commonly used one is the STFT or the spectrogram. STFT can easily display the variations in the sinusoidal frequency and phase content of local moments of a signal over time with sufficient resolution in most cases.

      The spectrogram transforms the signal onto two‐dimensional (2D) time‐frequency plane via the following famous equation:

      (1.17)equation

      This transformation formula is nothing but the short‐time (or short‐term) version of the famous FT operation defined in Eq. 1.1. The main signal, g(t) is multiplied with a shorter duration window signal, w(t). By sliding this window signal over g(t) and taking the FT of the product, only the frequency content for the windowed version of the original signal is acquired. Therefore, after completing the sliding process over the whole duration of the time‐domain signal g(t) and putting corresponding FTs side by side, the 2D STFT of g(t) is obtained.

      It is obvious that STFT will produce different output signals for different duration windows. The duration of the window affects the resolutions in both domains. While a very short‐duration time window provides a good resolution in the time direction, the resolution in the frequency direction becomes poor. This is because of the fact that the time duration and the frequency bandwidth of a signal are inversely proportional to each other. Similarly, a long duration time signal will give a good resolution in frequency domain while the resolution in the time domain will be bad. Therefore, a reasonable selection has to be bargained about the duration of the window in time to be able to view both domains with fairly good enough resolutions.

Graph depicts time-frequency representation of the word prince. Schematic illustrations of scattering mechanisms in the joint time–frequency plane. (a) Scattering center, (b) resonance, (c and d) dispersion due to material, (e and f) dispersion due to geometry of the structure. Graph depicts the JTF image of a backscattered 
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