By M. Schetzen

The e-book starts off with a uncomplicated dialogue of the Doppler impression and its numerous 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 obstacles. A precis of the mathematical thoughts required for improvement of an actual idea is then offered utilizing the case of a slender beam antenna. this is often through the advance of the precise concept for the overall case, that's graphically illustrated and in comparison with the quasi-static approximation. common stipulations for which the quasi-static approximation errors will be over the top – particularly as utilized to laser Doppler radars and low-flying airplane – are presented.

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**Sample text**

Quasi-static Approximation From the above discussion, the quasi-static approximation of the Doppler spectrum is to assign to each point on the terrain a Doppler frequency that corresponds to the rate of change of the radial distance to that point and to calculate the spectrum in a given frequency interval by summing the total power received from all inﬁnitesimal regions with an assigned frequency in that interval. Note that this assumes that reﬂections from the various scatterers are uncorrelated so that the total power of the echo received by the Doppler radar is equal to the sum of the powers received from the individual scatterers.

The 3-dB bandwidth will be proportional to sqs but, as will be seen from our discussion, its exact Fig. 5 Normalized quasi-static Doppler frequency versus s1. QUASI-STATIC APPROXIMATION OF THE DOPPLER SPECTRUM 47 Fig. 6 Normalized quasi-static Doppler frequency versus the rotation angle, f. value is not really needed. However, the value of the proportionality factor can be calculated from the shape of the quasi-static Doppler spectrum, which can be determined from Eq. 8). First, as discussed, sqs and dqs do not vary with height.

Clearly, if T is a period, then so is nT in which n ¼ 1, 2, 3, . . The smallest value of T ¼ T1 is called the fundamental period of p(t). If a waveform p(t) is periodic with a fundamental period T1, then, with certain mild conditions that are met by physical waveforms, it can be expressed as the linear combination of sinusoids with the harmonic frequencies vn ¼ nv1 in which v1 ¼ 2p=T1 as p(t) ¼ 1 X An cos (vn t) þ Bn sin (vn t) n¼0 This expression is called the Fourier series of the periodic waveform p(t).