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EE1003_ClassroomExercise1 - term i.e v t = A cos(2 πf t A...

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Classroom Exercise #1 Here’s the exercise that we did in class today. Problem: Draw the amplitude spectrum of v ( t ) = A cos(2 πf 0 t ) + A 2 cos(4 πf 0 t ) . Solution: Applying the fact that cos( θ ) = 1 2 ( e + e - ) , we have the following expansion: v ( t ) = A 2 e j 2 πf 0 t Phasor 1 + A 2 e j 2 π ( - f 0 ) t Phasor 2 + A 4 e j 2 π (2 f 0 ) t Phasor 3 + A 4 e j 2 π ( - 2 f 0 ) t Phasor 4 This expansion yields the following amplitude spectrum of v ( t ) . Further Discussion: Suppose we extend the above problem by adding yet another cosine
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Unformatted text preview: term, i.e., v ( t ) = A cos(2 πf t ) + A 2 cos(4 πf t ) + A 4 cos(6 πf t ) . What will the amplitude spectrum look like? Answer: There should be two additional spectral lines added to the above amplitude spectrum. Both will have height A 8 , but one will be centered at 3 f , the other at-3 f ....
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