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Unformatted text preview: Preliminary Exam II Solution (ECE220 - Fall 2007) Name: Solution NetID: QED • This exam is purely technical and does not leave much space for the imagination. Write the equations that lead to the result rather than trying to guess. Only after you have gone methodically through the derivation, try to see if it makes sense intuitively. • Reasoning and work must be shown to gain full/partial credit. • This exam is closed book and closed note. • WRITE YOUR NAME AND NET ID ON ALL PAGES HANDED IN! Name: Solution NetID: QED 1. (60 points) Consider the following two systems Let h 1 ( t ) = δ ( t- T ) and h 2 ( t ) = 1 T rect ( t T ). (a) (30 points) Calculate their impulse response. Solution: i) h ( t ) = h 1 ( t ) * h 2 ( t ) = δ ( t- T ) * 1 T rect ( t T ) = R ∞-∞ δ ( τ- T ) 1 T rect ( t- τ T ) dτ = 1 T rect ( t- T T ) ii) h ( t ) = h 1 ( t ) + h 2 ( t ) = δ ( t- T ) + 1 T rect ( t T ) (b) (30 points) Calculate their frequency response....
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