By M. Schetzen
The publication starts off with a uncomplicated dialogue of the Doppler influence 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 knowing of the approximation and its boundaries. A precis of the mathematical recommendations required for improvement of a precise idea is then provided utilizing the case of a slim beam antenna. this can be through the improvement of the precise thought for the overall case, that's graphically illustrated and in comparison with the quasi-static approximation. common stipulations for which the quasi-static approximation blunders will be over the top – particularly as utilized to laser Doppler radars and low-flying airplane – are presented.
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Extra resources for Airborne Doppler Radar
The reason for this normalization is that the graphs are then independent of wavelength and aircraft velocity. Furthermore, for convenience in using the graphs, dqs is in hertz. From Eq. 6) the normalized frequency assigned to the beam center thus is 2 sin ue cos ua cycles. 3 is a graph of the normalized quasi-static Doppler frequency versus the elevation angle ue for the azimuth angle ua ¼ 0, 25, 50, and 75 degrees. 4 is a graph of the normalized quasi-static Doppler frequency versus the azimuth angle ua for the elevation angle ue ¼ 5, 30, 55, and 80 degrees.
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.
7) and Eq. 8), are called a Fourier transform pair. They are a pair because, if one is true, then so is the other. For example, let F( jv) be determined using a given function f (t) in Eq. 8). Then if F( jv) were used in Eq. 7), the integration would result in the same function f (t) used in Eq. 2 The function f (t) is thus called the inverse Fourier transform of F( jv). 9) is satisﬁed for the Fourier transform theory we shall discuss. As a simple example, let f (t) ¼ eÀa t u(t) (5:10) in which a .
Airborne Doppler Radar by M. Schetzen