By M. Schetzen
The publication starts with a simple dialogue of the Doppler influence and its a number of purposes, 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 besides illustrations and discussions to assist the reader achieve an intuitive knowing of the approximation and its obstacles. A precis of the mathematical ideas required for improvement of an actual concept is then awarded utilizing the case of a slim beam antenna. this is often through the improvement of the precise concept for the overall case, that's graphically illustrated and in comparison with the quasi-static approximation. basic stipulations for which the quasi-static approximation errors will be over the top – in particular as utilized to laser Doppler radars and low-flying plane – are presented.
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Additional resources for Airborne Doppler Radar
The properties we need will be presented later in this pre´cis in the context in which they’ll be used so that they can be interpreted in a manner that is physically meaningful in the application. However, there is one other property that we’ll obtain here. 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).
Introduction N ORDER to clearly discuss how Doppler radar can be used for aircraft navigation and stabilization, the echo obtained by an aircraft Doppler radar in Chapter 3 was considered to be a sinusoid with a constant amplitude and frequency. The frequency of the echo was considered to be equal to that of the sinusoid transmitted by the Doppler radar transmitter displaced by an amount equal to the Doppler shift that would be obtained from an individual scatterer when it is at the center of the antenna beam.
To discuss how the Doppler effect can be used for the navigation (avigation) and stabilization of an aircraft, consider an aircraft ﬂying at an altitude h in the x direction with a velocity v as depicted in Fig. 1. Let the antenna of a CW Doppler radar on the aircraft be directed at the point p in the diagram. The CW Doppler radar transmits a sinusoidal wave with the frequency v0 . From Eq. 22), the Doppler shift is d¼À 2v0 dr c dt rad=s (3:2) From the diagram above, r 2 ¼ h2 þ rx2 þ ry2 . Because h and ry are ﬁxed we have 2r dr drx ¼ 2rx dt dt or dr rx drx rx ¼ ¼À v dt r dt r (3:3) Again from the diagram, we observe that rx ¼ r sin cr cos ca Fig.
Airborne Doppler Radar by M. Schetzen