The Uncertainty Principle

  • D. E. Vakman
Part of the Applied Physics and Engineering book series (APPLIED PHYS, volume 4)


It has thus far been assumed that the received signal is reflected from a stationary target so that the carrier frequency of the transmitted and reflected signals coincide. The general case will now be considered. Assume that the signal is reflected from a target whose range is r0, and whose range rate is v0. Thus the reflected signal is delayed by the time t0 = 2r0/c and acquires a Doppler shift of Q = (2v0/c) ω0:
$$ {s_{1}}\left( t \right) = s\left( {t - {t_{0}}} \right){e^{{j\Omega \left( {t - {t_{0}}} \right)}}} $$


Wave Packet Range Rate Uncertainty Principle Instantaneous Frequency Impulse Response Function 
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© Springer-Verlag New York Inc. 1968

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  • D. E. Vakman

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