A chirp signal, in which the angular frequency rises uniformly from Ï 0 ÎÏ/2 to Ï 0

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A chirp signal, in which the angular frequency rises uniformly from ω0€“Δω/2 to ω0+ Δω/2 over a time T, can be written as exp(iφ(t)), where the phase φ(t) is given by


Δω φ()- ωρΐ + 27


for |t| ‰¤ T/2. This signal is then passed through a delay-line, whose effect on a component of angular frequency w can be represented as multiplication by the factor 


exp( - io(T/До) (00 + o/2)


Show that the signal that emerges from the delay-line is a carrier of angular frequency ω0, modulated by an envelope of width 2π/Δω.

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