Inverse Synthetic Aperture Radar Imaging With MATLAB Algorithms. Caner Ozdemir

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1.30. The sampling theorem can be applied in the following manner:

      Suppose that target to be imaged lies in the range direction within the range width or range extend of Rmax such that

      (1.33)equation

Graphs depict Nyquist sampling procedure for getting unaliased range image. (a) Frequency-domain radar signal for a range windowed data, (b) range domain signal, (c) sampling comb signal in frequency domain, (d) its range domain equivalent, (e) critically sampled version of the frequency-domain signal, and (f) its range domain equivalent.

      (1.34)equation

      where c is the speed of light. Utilizing the relationship between the wave‐number; k and the distance; R in Eq. 1.30, the sampling in the wave number domain should satisfy the following inequality:

      (1.35)equation

      This inequality is forced by the famous Nyquist sampling condition. The minimum sampling frequency, then, should be equal to

      (1.36)equation

      Then, the sampled version of frequency‐domain signal G(f) is obtained by the multiplication of the G(f) with the following impulse comb function:

      (1.37)equation

      The plot of this comb function is shown in Figure 1.16c. By taking the IFT of this comb function, we can get another comb function in the range domain as

      (1.38)equation

      as depicted in Figure 1.16d. The sampled version of frequency‐domain signal, Gs(f) can be get by multiplying the original frequency‐domain signal, G(f) with the impulse comb function in Figure 1.16c as

      (1.39)equation

      that is shown in Figure 1.16e. The range domain equivalent of the frequency‐domain sampled signal can be found via inverse Fourier transforming as

      (1.40)equation

Graphs depict effect of sampling rate. (a) No aliasing due to oversampling and (b) aliased or distorted range domain waveform due to undersampling.

      Below are the Matlab source codes that were used to generate all of the Matlab‐produced figures in this chapter. The codes are also provided inside the CD of this book.

      Matlab code 1.1 Matlab file “Figure1‐1.m”_________________________________

      %‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ % This code can be used to generate Figure Figure 1.1 %‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ % This file requires the following files to be present in the same % directory: % %prince.wav clear all close all % Read the sound signal "prince.wav" [y,Fs] = audioread('prince.wav'); sound(y,Fs); %play the sound N=length(y); % TIME DOMAIN SIGNAL t=0:.8/(N-1):.8; %form time vector plot(t,y,'k'); %downsample for plotting grid minor set(gca,'FontName', 'Arial', 'FontSize',12, 'FontWeight','Bold'); axis tight; xlabel('time, s'); ylabel('amplitude'); title('\ittime domain signal');

      Matlab

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