{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

HW-12-solution - HW-12 1 In the complex notation there is a...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
HW-12 1. In the complex notation there is a clever device for finding the time average of a product. Suppose ) cos( ) , ( a t r k A t r f and ) cos( ) , ( b t r k B t r g . Show that *) ~ ~ Re( ) 2 / 1 ( g f fg , where f ~ and g ~ are the complex of f and g and the star denotes complex conjugation. Solution: First, let us perform a direct calculation fgdt T fg T 0 1 where 2 T is the periodicity. ) cos( 2 )] cos( 0 [ 2 )] cos( ) 2 2 [cos( 2 ) cos( ) cos( 1 1 0 0 0 b a b a b a b a T b a T T AB T T AB dt t r k T AB dt t r k B t r k A T fgdt T fg Second, let us calculate *) ~ ~ Re( g f . ) exp( ~ ), exp( ~ b a t r k B g t r k A f . Then ) cos( )] ( exp[ Re )] ( exp[ )] ( exp[ Re *) ~ ~ Re( b b b b b b AB i AB t r k i B t r k i A g f .
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}