General integral equation formulation for microstrip antennas and scatterers

Abstract

Generating accurate, high-resolution time-frequency distributions (TFD) is a critical aspect of dynamic radar scattering analysis. Well-formed TFD's can be used for target identification, target acquisition in high- INTRODUCTIONThe Fourier Transform has long been an important tool for providing a measure of the frequencies contained within a signal. Time-frequency distributions (TFD) extend the functionality of the Fourier Transform by computing the localized frequency content at a particular time within the signal. Thus, one can obtain information about the dynamic frequency-domain behavior of a signal over time. Within the realm of radar scattering, one can interpret the TFD physically as a representation of the dynamically changing Doppler frequency shifts caused by moving targets or targets with moving components. TFDs can then be used for a variety of applications, such as clutter reduction and moving target detection using airborne radars [1].As an example, consider the ẑ-directed dipole source spinning about the origin as shown in Figure 1(a), where we wish to measure the far field radiated in the negative x -direction [2]. From Doppler theory, we know that the frequency measured at the observation point will shift upwards when the source is approaching the observer. As the source recedes, the observed frequency shifts downward with the Doppler shift frequency given bySince v ϭ 2l (t), where is the usual cylindrical unit vector and t denotes time, the Doppler frequency as time increases can then be expressed as A TFD of this situation would then look as that shown in Figure 1(b). In practice, to generate Figure 1(b) we use the scattered signal from the rotating object. The simplest and most well known method for generating a given signal's TFD is the windowed Fourier transform known as the spectrogram [3]. Basically, to find the signal component associated with frequency at a certain time t, the received signal s(tЈ) is multiplied by a windowing function h(tЈ) centered at time t. The result is then transformed to frequency domain to yieldHere S t () is the spectrum of the windowed signal at time t. From Eq. (3), it is evident that a compact windowing function h will increase localization in time domain but lower resolution in frequency domain. Conversely, a wide windowing function will lead to high frequency resolution and low time localization. This uncertainty principle, present in all signal-processing TFD approaches, ultimately limits our overall resolution and forces us to settle for a compromise between time and frequency resolution. It is, of course, desirable to remove this restriction and allow for an arbitrary resolution in both domains.In proceeding to remove such a restriction, we note that Eq. (3) neglects information from the individual currents J, which are the source of the scattered field (see Fig. 2(a)). In this paper we present a physics-based approach called the Direct TFD (DTFD) for computing each column of the TFD from knowledge of the individual currents upon the geometry ...

An efficient perfectly matched layer based multilevel fast multipole algorithm for large planar microwave structures

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Application of a simplified probe feed impedance formula to the design of a dual frequency patch antenna

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