3.2卫 Rate at which Ige-70 for k large determines smoothness The above figures show two functions together with a plot of the amplitude of their Fc important feature of the Fourier coefficients Chat they are directly as sociated with the smoothness of the original function we can intuitively see that the less oscillatory the function, the faster Ige will tend to zero as k becomes large, since we will need less "high frequency"(small wavelength)contributions 3.3 Differentiation SLIDE 12 u(m)=∑ a(a, t) k t)✽✰✾❀✿ ❁❃❂❅❄❇❆❉❈❋❊❍● ■❑❏✯▲◆▼☛❖✶P✪◗ 0 1 2 3 4 5 6 −0.5 0 0.5 1 1.5 2 2.5 x g(x) g1(x) g2(x) ■❑❏✯▲◆▼☛❖✶P❘P 1 2 3 4 5 6 7 8 9 10 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 k |Ck| g1(x) g2(x) ❙❯❚✪❱❳❲❨❚✪❱✰❩❅❬✗❭✒❪❫❬❵❴ ❛✁❜❝❴✖❞❢❡✴❣☞❤✖✐❥❴ ❦❧❴✯♠✏❚✪✐✱♥✖❲✝♦❝❲✟❱✱❲♣✐✱q✧❭sr❘❲☎t❯✉☎✈❵✇❧✇✍①★②④③✄⑤⑥✉☎✉ ⑦⑨⑧❘⑩❷❶✖❸❫❹✪❺❻⑩❋❼✄❽✖❾❝❿❳⑩✟➀✧➀✓⑧✗❹✕➁➃➂➄➁➅❹✑➆❫❾❝➇❑➈♣➂❀➉➊❹✪➇❘➀➋➂➌❹✱❽✯⑩✟➂☞⑧❘⑩♣❿➍➁➎➉◆➂☞⑧❵❶➋➏❑➐s❹✪➂✡❹✓➆➋➂☞⑧❘⑩❷❶✕➑➒➏❑➐➓➉◆➂➄❾✗➔✖⑩❷❹✓➆ ➂☞⑧❘⑩♣➉◆❿➍→✄❹✕❾❝❿➣➉➊⑩♣❿✸➈✱❹☎⑩❀↔↕➈♣➉➊⑩✟➇✍➂➊➀♣➙✜➛✻➇➜➉◆➑➒➏❘❹✪❿➣➂➌❶✪➇✗➂➅➆✟⑩❫❶✪➂❀❾❝❿❳⑩➝❹❍➆❷➂☞⑧❘⑩➞→✄❹✕❾❝❿➣➉➊⑩♣❿✚➈✱❹☎⑩❀↔↕➈♣➉➊⑩✟➇✍➂➊➀❷➉✏➀ ➂☞⑧❘❶✕➂✡➂☞⑧❘⑩♣➟➠❶✪❿❳⑩✸➔✕➉◆❿✱⑩✱➈♣➂➄➐➓➟✤❶✕➀❫➀✟❹☎➈♣➉➊❶✕➂➡⑩✱➔➢➁➎➉◆➂◆⑧➤➂☞⑧❘⑩❃➀➣➑➋❹★❹✪➂◆⑧❝➇❑⑩✟➀✱➀❷❹❍➆➥➂◆⑧✗⑩✸❹✕❿➣➉➦❽✖➉◆➇❑❶✕➐❧➆❫❾❝➇⑨➈✟➂➄➉➊❹✕➇⑨➧ ➁➅⑩➞➈❫❶✪➇➢➉◆➇✗➂➄❾❝➉◆➂❀➉◆❺✕⑩✟➐➦➟➥➀♣⑩❫⑩➋➂☞⑧❘❶✪➂❯➂☞⑧❘⑩➋➐✒⑩➣➀❫➀➍❹❻➀♣➈✟➉◆➐◆➐✒❶✕➂➡❹✕❿➣➟✸➂☞⑧❘⑩❯➆❫❾❝➇⑨➈✟➂➄➉➊❹✕➇✗➨❯➂◆⑧✗⑩❯➆✟❶✕➀❫➂➡⑩♣❿➋❴ ❛✁❜❝❴➎➁➎➉◆➐◆➐ ➂➡⑩✟➇⑨➔❨➂➡❹❋➩☎⑩♣❿❳❹✴❶❻➀❋❴ ❦❧❴⑨❸❫⑩✱➈❫❹✪➑✧⑩✟➀➒➐s❶✪❿❀❽✁⑩✟➨④➀❫➉◆➇⑨➈❫⑩➒➁➅⑩❋➁➎➉◆➐◆➐❑➇❑⑩❫⑩❫➔❥➐s⑩➣➀❫➀➝➫☞⑧⑥➉➦❽❻⑧✻➆❫❿❳⑩❫➭✟❾✗⑩♣➇❑➈♣➟✍➯❥➲➄➀❫➑➋❶✕➐◆➐ ➁➅❶✕❺✕⑩♣➐s⑩✟➇⑥❽✪➂☞⑧☎➳➥➈❫❹✪➇✗➂➄❿➣➉➊❸✟❾❝➂➄➉➊❹✕➇✗➀✟➙ ✽✰✾❀✽ ➵✜➸❍➺❨●❧➻❘●☛➼✔➽❘➸❍❄④➽❘➸❍➾➅➼ ■❑❏✯▲◆▼☛❖✶P✖➚ ➪④➶➊➹❑➘➷➴ ➮➬ ❜➣➱❇✃ ➬ ➪ ❜❒❐❻❮ ❜➣❰ ✇✗Ï ➪④➶➊➹☛Ð✓Ñ✓➘➷➴ ➮➬ ❜➣➱❇✃ ➬ ➪❜ ➶➊Ñ✓➘ ❐❻❮ ❜➣❰ Ò⑨Ó ➪ Ò ➹Ó ➴ ➮➬ ❜➣➱❇✃ ➬ ➶☞Ô ❦ ➘ Ó ➪ ❜❒❐ ❮ ❜➣❰ Ò ➪ Ò Ñ ➴ ➮➬ ❜➣➱❇✃ ➬ Õ➪❜ Õ Ñ ❐ ❮ ❜➣❰ Ö ➴ ×✕Ø ❞ ➶☞Ô ❦ ➘ Ó ➴ ➶❍Ù✡Ú☎➘✓Û ❦❝ÜÛ ➶ ✐✱❲★❚✖♠ ➘ Ö ➴ ×✕ØÝÙ↕Ú ❞ ➶☞Ô ❦ ➘ Ó ➴ Ù❅Ô❫➶✓Ù✡Ú☎➘✓Û ❦❝ÜÛ ✃❧Þ ➶ ❭✒q➋❚✪♥✖❭✒r✗❚✖✐❳ß➘ Ú ❡