Heimadaemi_01_lausnir

Heimadaemi_01_lausnir - A F5GF ja Ö×k iÔ ØaÚ e Ök...

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Unformatted text preview: A F5GF ja Ö×k iÔ ØaÚ e Ök fÖð i e iÑ adÑ i aÙ ×Ò iÖ Öe fÒaa Ö íÒG ÙÒÒa Ö×dó ØØ iÖ aÙ ×Ø DÑ i F ÓÙ Ö ieÖÚö ÖÔÙÒ g ( t ) eÖ G ( f ) g ( t ) ←→ G ( f ) aÒÒ iðe fØ iÖ fa ÖaÒd i: E f g ( t ) eÖÖaÙÒg iÐØÓg ja fÒ ×ØØØþeÖ G ( f ) ÖaÙÒg iÐØÓg ja fÒ ×ØØØ E f g ( t ) eÖÖaÙÒg iÐØÓgÓdd ×ØØØþeÖ G ( f ) ØÚ iÒÒ Øa ÐaÓgÓdd ×ØØØ aÙ ×Ò : G ( f ) = integraldisplay ∞-∞ g ( t ) e- j 2 πft dt = integraldisplay ∞ g ( t )( e- j 2 πft + e j 2 πft ) dt, þÚ í g ( t ) = g (- t ) = 2 integraldisplay ∞ g ( t ) cos(2 πft ) dt a Ö×eÑ g Ø eÖÖaÙÒg iÐØþeÖ G ( f ) Ðíka ÖaÙÒg iÐØa Ö×eÑ cos(2 πft ) = cos(- 2 πft ) eÖja fÒ ×ØØØþeÖ G ( f ) = G (- f ) Óg ja fÒ ×ØØØ G ( f ) = integraldisplay ∞-∞ g ( t ) e- j 2 πft dt = integraldisplay ∞ g ( t )( e- j 2 πft- e j 2 πft ) dt, þÚ í g ( t ) =- g (- t ) = 2 j integraldisplay ∞ g ( t ) sin(2 πft ) dt a Ö×eÑ g Ø eÖÖaÙÒg iÐØþeÖ G ( f ) ØÚ iÒÒ Øa Ða h éÖÒÓ Øað íÑ eÖk iÒgÙÒÒ ih Öe iÒþÚ eÖØa Ða a Ö ×eÑ sin(2 πft ) =- sin(- 2 πft ) eÖÓdd ×ØØØþeÖ G ( f ) =- G (- f ) ÓgÓdd ×ØØØ DÑ i Ñ ÐÓ ØÙbÙÒd iðÑ eÖk ig iÐd iÖað g ( t ) =- g ( t + T / 2) þaðeÖ× íða Ö ih e ÐÑ iÒgÙ ÖhÚ eÖÖa Ö ÐÓ ØÙ eÖ Ò e ikÚðú Øg faa ffÝ ÖÖ ih e ÐÑ iÒg ÐÓ ØÙÒÒa ÖýÒ iðaðþeÖ c n = 0 þ ega Ö n eÖ× ÐéØØØa Ða × j jö fÒÙ 8 íbók aÙ ×Ò :ið×k iÔ ØÙÑ Øeg Ö iÒÙ fÝ Ö iÖ c n ÙÔÔ íØÚÓh ÐÙ ØaÓgÒý ØÙÑ ÓkkÙ Ö×aÑ hÚ eÖ fÙg Ø ×eÑ eÖ ÐÓ ØÙbÙÒd iðÑ eð ÐÓ ØÙ T FÙÑ : c n = 1 T bracketleftBigg integraldisplay T / 2 g ( t ) e- j 2 πnf t dt + integraldisplay T T / 2 g ( t ) e- j 2 πnf t dt bracketrightBigg = 1 T bracketleftBigg integraldisplay T / 2 g ( t ) e- j 2 πnf t dt + integraldisplay...
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Heimadaemi_01_lausnir - A F5GF ja Ö×k iÔ ØaÚ e Ök...

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