Applications of the joint time-frequency transforms on inverse problems in electromagnetics

Two novel joint time-frequency transforms (JTFTs) are introduced and investigated. Both methods combine the advantages of a joint time-frequency signal representation with the properties of spectral estimation techniques. In particular, the PDFT algorithm, a linear spectral estimation technique, is used to replace the discrete Fourier transform operation of the short time Fourier transform (STFT) and the Wigner Ville distribution (WVD). The novel JTFTs, which are termed ‘short time PDFT’ (STPDFT) and Wigner PDFT (WPDFT) are aimed at providing enhanced estimation of the instantaneous signal frequency.; The performance of both the STPDFT as well as the WPDFT is evaluated based on synthesized signals. While both methods provide a significantly improved resolution of the joint time-frequency plane, the STPDFT is shown to be more attractive for practical signal processing problems. This is due to the fact the STPDFT is a linear method (as compared to the nonlinear WPDFT transformation) and computationally more efficient.; The novel JTFTs are then applied to inverse synthetic aperture radar imaging. Due to the numerical complexity of the WPDFT only the STPDFT is applied extensively to measured data and synthetic data which simulate realistic imaging problems. In order to evaluate the performance of the STPDFT algorithm it is applied to imaging problems which have been addressed successfully with JTFTs before. In particular, this includes the problem of motion blur in inverse synthetic radar imaging. The performance of the STPDFT algorithm is compared with the results obtained with other JTFTs. The results prove the concept of improved resolution in the JTFT domain, with acceptable numerical complexity.; In addition, the STPDFT algorithm is applied to low resolution radar data acquired in the context of foliage penetration radar imaging. In this case the JTFTs are used as heuristic measures to improve the target to background ratio and to enhance target features. Again, it is possible to confirm the good performance of the STPDFT algorithm as compared to alternative JTFTs.