Note #10

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* H/W 1 Problem #2Similarly,If X(t) is odd it implies X(-t) = -X(t)Prove:α m = 0To /2β m = 2*(2/ To) X ( t)sin2πmfo∫tdt0

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So,αTo /2∫2*(2/ T ) X( t)cos2mπf tdtm =o o00 To /2m = (2/ o) ( )sin 2 o + (2/ o) ( )sin 2 o∫β T X t mπ f tdt T X t mπf tdtTo /2 0∫(for y=-t)=0 To /2∫ ∫(2/ To) X( −y)sin−2 πmfoy( − dy) + (2/ To) X( t)sin 2mπfotdtTo /2 0putting X(-y) = X(y)=0 To /2∫ ∫(2/ To) X( y)sin 2 πmfoydy + (2/ To) X( t)sin 2mπfotdtTo /2 0change= -0 To /2∫ ∫(2/ To) X( y)sin 2 πmfoydy + (2/ To) X( t)sin 2mπfotdtTo /2 0= 0

* H/W 1 Problem #2Similarly,If X(t) is odd it implies X(-t) = -X(t)Prove:α m = 0To /2β m = 2*(2/ To) X ( t)sin2πmfo∫tdt0

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Note #10

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