Inverse Synthetic Aperture Radar Imaging With MATLAB Algorithms. Caner Ozdemir

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      (1.18)equation

      In a dual manner, convolution between the frequency‐domain signals can be calculated in a much faster and easier way by taking the FT of the product of their time‐domain versions as formulated below:

      (1.19)equation

      Filtering is the common procedure that is used to remove undesired parts of signals such as noise. It is also used to extract some useful features of the signals. The filtering function is usually in the form of a window in the frequency domain. Depending on the frequency inclusion of the window in the frequency axis, the filters are named low‐pass (LP), high‐pass (HP), or band‐pass (BP).

Graph depicts the ideal and real LP filter characteristics. Graph depicts the common window characteristics. Schematic illustrations of windowing. (a) Rectangular time signal, (b) its Fourier spectrum: a sinc signal, (c) Hanning windowed time signal, (d) corresponding frequency-domain signal.

      A main drawback of windowing is the resolution decline in the frequency signal. The FT of the windowed signal has worse resolution than the FT of the original time‐domain signal. This feature can also be noticed from the example in Figure 1.8. By comparing the main lobes of the figures on the right, the resolution after windowing is almost twice as bad when compared to the original frequency‐domain signal. A comprehensive examination of windowing procedure will be presented later on, in Chapter 5.

      

Graphs depict the (a) continuous time signal, (b) discrete-time signal after the sampling.

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