By M. Schetzen
The e-book starts off with a easy dialogue of the Doppler influence and its numerous purposes, and the way Doppler radar can be utilized for the stabilization and navigation of plane. A quasi-static approximation of the Doppler spectrum is gifted besides illustrations and discussions to aid the reader achieve an intuitive realizing of the approximation and its obstacles. A precis of the mathematical ideas required for improvement of a precise idea is then offered utilizing the case of a slender beam antenna. this is often by means of the advance of the precise thought for the overall case, that is graphically illustrated and in comparison with the quasi-static approximation. common stipulations for which the quasi-static approximation blunders will be over the top – in particular as utilized to laser Doppler radars and low-flying airplane – are presented.
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Extra info for Airborne Doppler Radar
1 percent of c (c % 186,300 miles/s). In the atmosphere, this corresponds to velocities less than 26,268 miles per second! 2 The nonrelativistic Doppler shift for sonic waves is different than that for electromagnetic waves because sonic waves can only travel in a medium. Because sonic velocities are so much less than the velocity of light, we only need to consider the nonrelativistic theory for the Doppler shift of sonic waves. To obtain the equations for the Doppler shift, we consider the situation in which a source is traveling at a constant velocity ns directly toward a receiver that also is traveling at a constant velocity nr directly toward the source.
1 1 1 3 % v0 1 þ b À b2 1 þ b þ b2 2 8 2 8 (2:12) Keeping only terms to the second power of b, we obtain 1 2 v % v0 1 þ b þ b 2 (2:13) To a ﬁrst power of b, this is the nonrelativistic result given by Eq. 10). 1 percent of c (c % 186,300 miles/s). In the atmosphere, this corresponds to velocities less than 26,268 miles per second! 2 The nonrelativistic Doppler shift for sonic waves is different than that for electromagnetic waves because sonic waves can only travel in a medium. Because sonic velocities are so much less than the velocity of light, we only need to consider the nonrelativistic theory for the Doppler shift of sonic waves.
It is a condition that is sufﬁcient but not necessary to assure the convergence of all integrals. The two-dimensional Fourier transform is obtained by determining the transform of f2 (t1 , t2 ) with respect to one variable at a time. By holding the variable t2 constant, the one-dimensional Fourier transform is F1 ( jv1 , t2 ) ¼ ð1 À1 f2 (t1 , t2 )eÀjv1 t1 dt1 (5:27) Now by holding the variable v1 constant, the one-dimensional Fourier transform of F1 ( jv1 , t2 ) with respect to t2 is F2 ( jv1 , jv2 ) ¼ ¼ ð1 À1 ð1 À1 F1 ( jv1 , t2 )eÀjv2 t2 dt2 ð1 À1 f2 (t, t2 )eÀjv1 t1 eÀjv2 t2 dt1 dt2 (5:28) This last equation is obtained by substituting Eq.
Airborne Doppler Radar by M. Schetzen