By M. Schetzen

The publication starts off with a simple dialogue of the Doppler influence and its a variety 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 besides illustrations and discussions to assist the reader achieve an intuitive realizing of the approximation and its barriers. A precis of the mathematical recommendations required for improvement of a precise conception is then offered utilizing the case of a slender beam antenna. this can be via the advance of the precise idea for the final case, that's graphically illustrated and in comparison with the quasi-static approximation. normal stipulations for which the quasi-static approximation mistakes will be over the top – particularly as utilized to laser Doppler radars and low-flying plane – are presented.

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**Extra resources for Airborne Doppler Radar**

**Example text**

Because the quasi-static Doppler bandwidth is a measure of the variation of d(cr , ca ) over the region illuminated by the antenna, there should be an QUASI-STATIC APPROXIMATION OF THE DOPPLER SPECTRUM 49 Fig. 9 Normalized quasi-static Doppler bandwidth versus s1. orientation of the antenna pattern ellipse for which the bandwidth is a minimum. This minimum should be at an angle at which the major elliptical axis lies tangent to an isodoppler. An isodoppler is a curve along which the Doppler d(cr , ca ) is a constant.

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. The source transmits a sonic wave that, as before, is a sinusoidal wave given by Eq. 1). The wave that travels through the medium will contain a sequence of crests traveling through the medium at a velocity of c, which is the sonic wave velocity in the medium. For our derivation, we ﬁrst consider the case in which nr ¼ 0 so that only the source is moving.

The reason is that the echo is the sum of the reﬂections from many terrain particles in the antenna beam. Observe that dr=dt varies as a particle travels through the antenna beam and it also differs from particle to particle. In addition, the return from a given particle is amplitude modulated by the antenna pattern and with the manner in which the backscattering from the particle varies with angle. We thus can view the echo as a complex waveform that is the sum of many sinusoids, each of which has been amplitude and frequency modulated.