New PDF release: Airborne Doppler Radar
By M. Schetzen
The ebook starts with a easy dialogue of the Doppler impression and its a number of functions, and the way Doppler radar can be utilized for the stabilization and navigation of airplane. A quasi-static approximation of the Doppler spectrum is gifted in addition to illustrations and discussions to assist the reader achieve an intuitive figuring out of the approximation and its boundaries. A precis of the mathematical techniques required for improvement of a precise conception is then provided utilizing the case of a slender beam antenna. this can be via the advance of the precise thought for the final case, that's graphically illustrated and in comparison with the quasi-static approximation. normal stipulations for which the quasi-static approximation errors will be over the top – particularly as utilized to laser Doppler radars and low-flying plane – are presented.
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The properties also lend a great deal of insight and understanding of the results obtained. 14 we then immediately have 1 1 G( jv) ¼ F½ j(v À v0 ) þ F½ j(v þ v0 ) 2 2 (5:18) As an illustration, with f (t) given by Eq. 10), we then have g(t) ¼ eÀat cos (v0 t) u(t) (5:19) ´ CIS OF WAVEFORM ANALYSIS TECHNIQUES PRE 57 so that, with the result given by Eq. 12), we obtain G( jv) ¼ ¼ 1 1 1 1 þ 2 a þ j(v À v0 ) 2 a þ j(v þ v0 ) a þ jv ½a þ j(v þ v0 )½a þ j(v À v0 ) (5:20) In addition to simplifying calculations as above, a great deal of insight into Fourier transforms can be obtained from their various properties.
53 degrees. 1 degrees with the rotation angle f ¼ 0, the azimuth angle ua ¼ 60 degrees, and the elevation angle ue ¼ 30 degrees. As expected, dqs is not a strong function of the beamwidth. Also, as discussed previously, dqs does not vary with height. 6 is a graph of the normalized quasi-static Doppler frequency versus the rotation angle f of the antenna ellipse for s1 ¼ 2 degrees and s2 ¼ 1 degree with the azimuth angle ua ¼ 60 degrees and the elevation angle ue ¼ 30 degrees. Note that the quasi-static Doppler frequency is not a strong function of f as we should expect because it is not a strong function of the beamwidth.
The property is that the Fourier transform of the conjugate of f (Àt) is the conjugate of F( jv). To obtain this property, we have from Eq. Ã dt ¼ À1 ð1 f Ã (t)eþjvt dt (5:21) À1 Thus, with the change of variable t ¼ Àt in the integral we obtain F Ã ( jv) ¼ ð1 f Ã (Àt)eÀjvt dt (5:22) À1 We thus observe that the Fourier transform of f Ã (Àt) is F Ã ( jv). As an example of the use of this property, we’ll determine the Fourier transform of s(t) ¼ eÀajtj in which a . 0 (5:23) With the use of the step function deﬁned by Eq.
Airborne Doppler Radar by M. Schetzen