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Topics in harmonic analysis with
Sonar and radar echo structure
The synthesis problem for radar ambiguity functions
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affine group amplitude analysis approximation array basis boundary condition bounded compact complex computation constant continuous function Corollary corresponding Costas array cross-ambiguity function CW mode field defined denotes derive dirichlet function doppler echo prediction electromagnetic equation equivalent expansion finite groups follows formula Fourier transform frame frequency given Green's theorem group G Heisenberg group Hence Hilbert space identity implies inner product integral representation invariant inverse irred unitary reps lattice Hilbert space Lemma Lie group linear Lie group mapping Mathematics matrix elements matrix reps nonzero one-dimensional oo oo oo orthogonality relations parameters phase plane wave projection-slice theorem Proof properties pulse mode pulse s(t pulse train Radar Ambiguity Functions radar echoes radiation Radon transform range reflector rep of G satisfies solution sonar Sonar Echoes square integrable subgroup subspace term theory transmitter unique unitary irred reps unitary operator vector velocity Verify Volume waveform wavelet zero