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# hw2 - EE 200L Homework 2 – G Caire – 1 USC EE 200L –...

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Unformatted text preview: EE 200L Homework 2 – G. Caire – September 18, 2009 1 USC EE 200L – Foundations of Electrical Engineering Systems – Fall 2009 Homework 2 Due date: Thursday, September 24, at 12:00 PM at the beginning of the class. Please drop your paper on the instructor’s desk. 1. Consider a transmitter located at position 0 (origin) on the real line, a reflector in position d , and a mobile receiver (e.g., a car) located at the time-dependent position r ( t ) = r + vt , where 0 < r < d , and v is the mobile speed. The transmitter sends a sinusoidal signal x ( t ) = A cos(2 πf t ) The mobile receiver gets the superposition of two delayed copies of the signal, due to the direct propagation from transmitter to receiver and to the reflected path propagation (transmitter, reflector, receiver). The received signal is given by y ( t ) = x ( t- τ ( t )) + αx ( t- τ 1 ( t )) where α ∈ R is the reflection coefficient, and where τ ( t ) and τ 1 ( t ) are the propagation delays along the direct and reflected paths. Letting c denote the light speed, we have that the propagation delay at some distance s is given by τ = s c . a) For the given geometry, write the expression of τ ( t ) and τ 1 ( t ) (as a functions of t , v , c , r and d )....
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hw2 - EE 200L Homework 2 – G Caire – 1 USC EE 200L –...

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