Build your knowledge of SAR/ISAR imaging with this comprehensive and insightful resource
The newly revised Second Edition of Inverse Synthetic Aperture Radar Imaging with MATLAB Algorithms covers in greater detail the fundamental and advanced topics necessary for a complete understanding of inverse synthetic aperture radar (ISAR) imaging and its concepts. Distinguished author and academician, Caner Özdemir, describes the practical aspects of ISAR imaging and presents illustrative examples of the radar signal processing algorithms used for ISAR imaging. The topics in each chapter are supplemented with MATLAB codes to assist readers in better understanding each of the principles discussed within the book.
This new edition incudes discussions of the most up-to-date topics to arise in the field of ISAR imaging and ISAR hardware design. The book provides a comprehensive analysis of advanced techniques like Fourier-based radar imaging algorithms, and motion compensation techniques along with radar fundamentals for readers new to the subject.
The author covers a wide variety of topics, including:
* Radar fundamentals, including concepts like radar cross section, maximum detectable range, frequency modulated continuous wave, and doppler frequency and pulsed radar
* The theoretical and practical aspects of signal processing algorithms used in ISAR imaging
* The numeric implementation of all necessary algorithms in MATLAB
* ISAR hardware, emerging topics on SAR/ISAR focusing algorithms such as bistatic ISAR imaging, polarimetric ISAR imaging, and near-field ISAR imaging,
* Applications of SAR/ISAR imaging techniques to other radar imaging problems such as thru-the-wall radar imaging and ground-penetrating radar imaging
Perfect for graduate students in the fields of electrical and electronics engineering, electromagnetism, imaging radar, and physics, Inverse Synthetic Aperture Radar Imaging With MATLAB Algorithms also belongs on the bookshelves of practicing researchers in the related areas looking for a useful resource to assist them in their day-to-day professional work.
CANER ÖZDEMIR, PHD, teaches undergraduate and graduate courses on electromagnetics, antennas, radar, and signal processing at Mersin University in Turkey. He has published over 150 scientific journal articles and is the recipient of the URSI EMT-S Young Scientist Award in the 2004 International Symposium on Electromagnetic Theory, as well as the 2016 Best Paper Award in SPIE-Journal of Applied Remote Sensing.
Basics of Fourier Analysis
1.1 Forward and Inverse Fourier Transform
Fourier transform (FT) is a common and useful mathematical tool that is utilized in innumerous applications in science and technology. FT is quite practical especially for characterizing nonlinear functions in nonlinear systems, analyzing random signals, and solving linear problems. FT is also a very important tool in radar imaging applications as we shall investigate in the forthcoming chapters of this book. Before starting to deal with the FT and inverse Fourier transform (IFT), a brief history of this useful linear operator, and its founders are presented.
1.1.1 Brief History of FT
Jean Baptiste Joseph Fourier, a great mathematician, was born in 1768, Auxerre, France. His special interest in heat conduction led him to describe a mathematical series of sine and cosine terms that could be used to analyze propagation and diffusion of heat in solid bodies. In 1807, he tried to share his innovative ideas with researchers by preparing an essay entitled as On the Propagation of Heat in Solid Bodies. The work was examined by Lagrange, Laplace, Monge, and Lacroix. Lagrange's oppositions caused the rejection of Fourier's paper. This unfortunate decision cost colleagues to wait for 15 more years to meet his remarkable contributions to mathematics, physics, and especially on signal analysis. Finally, his ideas were published thru the book The Analytic Theory of Heat in 1822 (Fourier 1955).
Discrete Fourier transform (DFT) was developed as an effective tool in calculating this transformation. However, computing FT with this tool in the nineteenth century was taking a long time. In 1903, C. Runge has studied on the minimization of the computational time of the transformation operation (Runge 1903). In 1942, Danielson and Lanczos had utilized the symmetry properties of FT to reduce the number of operations in DFT (Danielson and Lanczos 1942). Before the advent of digital computing technologies, James W. Cooley and John W. Tukey developed a fast method to reduce the computation time of DFT operation. In 1965, they published their technique that later on has become famous as the fast Fourier transform (FFT) (Cooley and Tukey 1965).
1.1.2 Forward FT Operation
The FT can be simply defined as a certain linear operator that maps functions or signals defined in one domain to other functions or signals in another domain. The common use of FT in electrical engineering is to transform signals from time domain to frequency domain or vice-versa. More precisely, forward FT decomposes a signal into a continuous spectrum of its frequency components such that the time signal is transformed to a frequency domain signal. In radar applications, these two opposing domains are usually represented as "spatial-frequency (or wave-number)" and "range (distance)." Such use of FT will be often examined and applied throughout this book.
The forward FT of a continuous signal g(t) where -8??<?t?<?8 is described as (1.1)
where represents the forward FT operation that is defined from time domain to frequency domain.
To appreciate the meaning of FT, the multiplying function exp(-j2pft) and operators (multiplication and integration) on the right of side of Eq. 1.1 should be examined carefully: The term is a complex phasor representation for a sinusoidal function with the single frequency of "fi." This signal oscillates with the single frequency of "fi" and does not contain any other frequency component. Multiplying the signal in interest, g(t) with provides the similarity between each signal, that is, how much of g(t) has the frequency content of "fi." Integrating this multiplication over all time instants from -8 to 8 will sum the "fi" contents of g(t) over all time instants to give G(fi) that is the amplitude of the signal at the particular frequency of "fi." Repeating this process for all the frequencies from -8 to 8 will provide the frequency spectrum of the signal represented as G(f). Therefore, the transformed signal represents the continuous spectrum of frequency components; i.e. representation of the signal in "frequency domain."
This transformation is the inverse operation of the FT. IFT, therefore, synthesizes a frequency-domain signal from its spectrum of frequency components to its time domain form. The IFT of a continuous signal G(f) where -8??<?f?<?8 is described as (1.2)
where the IFT operation from frequency domain to time domain is represented by .
1.2 FT Rules and Pairs
There are many useful Fourier rules and pairs that can be very helpful when applying the FT or IFT to different real-world applications. We will briefly revisit them to remind the properties of the FT to the reader. Provided that FT and IFT are defined as in Eqs. 1.1 and 1.2, respectively, FT pair is denoted as (1.3)
and the corresponding alternative pair is given by (1.4)
Based on these notations, the properties of FT are listed briefly below.
If G(f) and H(f) are the FTs of the time signals g(t) and h(t), respectively, the following equation is valid for the scalars a and b. (1.5)
Therefore, the FT is a linear operator.
1.2.2 Time Shifting
If the signal is shifted in time with a value of to, then the corresponding frequency signal will have the form of (1.6)
1.2.3 Frequency Shifting
If the time signal is multiplied by a phase term of , then the FT of this time signal is shifted in frequency by fo as given below (1.7)
If the time signal is scaled by a constant a, then the spectrum is also scaled with the following rule (1.8)
If the spectrum signal G(f) is taken as a time signal G(t), then, the corresponding frequency domain signal will be the time reversal equivalent of the original time domain signal, g(t) as (1.9)
1.2.6 Time Reversal
If the time is reversed for the time-domain signal, then the frequency is also reversed in the frequency domain signal. (1.10)
If the conjugate of the time-domain signal is taken, then the frequency-domain signal conjugated and frequency-reversed. (1.11)
If the time-domain signals, g(t) and h(t) are multiplied in time, then their spectrum signals G(f) and H(f) are convolved in frequency. (1.12)
If the time-domain signals, g(t) and h(t) are convolved in time, then their spectrum signals G(f) and H(f) are multiplied in the frequency domain. (1.13)
If the time-domain signal is modulated with sinusoidal functions, then the frequency-domain signal is shifted by the amount of the frequency at that particular sinusoidal function. (1.14)
1.2.11 Derivation and Integration
If the derivative or integration of a time-domain signal is taken, then the corresponding frequency-domain signal is given as below. (1.15)
1.2.12 Parseval's Relationship
A useful property that was claimed by Parseval is that since the FT (or IFT) operation maps a signal in one domain to another domain, their energies should be exactly the same as given by the following relationship. (1.16)
1.3 Time-Frequency Representation of a Signal
While the FT concept can be successfully utilized for the stationary signals, there are many real-world signals whose frequency contents vary over time. To be able to display these frequency variations over time; therefore, joint time-frequency (JTF) transforms/representations are being used.
1.3.1 Signal in the Time Domain
The term "time domain" is used while describing functions or physical signals with respect to time either continuous or discrete. The time-domain signals are usually more comprehensible than the frequency-domain signals since most of the real-world signals are recorded and displayed versus time. Common equipment is to analyze time-domain signals is the oscilloscope. In Figure 1.1, a time-domain...