Signals and Systems Collection Editor: Richard Baraniuk Signals and Systems Collection Editor: Richard Baraniuk Authors: Thanos Antoulas Richard Baraniuk Steven Cox Benjamin Fite Roy Ha Michael Haag Matthew Hutchinson Don Johnson Ricardo Radaelli-Sanchez Justin Romberg Phil Schniter Melissa Selik JP Slavinsky Online: <http://cnx.org/content/col10064/1.11/ > C O N N E X I O N S Rice University, Houston, Texas ➞✷✵✵✽ ❘✐❝❤❛r❞ ❇❛r❛♥✐✉❦ ❚❤✐s s❡❧❡❝t✐♦♥ ❛♥❞ ❛rr❛♥❣❡♠❡♥t ♦❢ ❝♦♥t❡♥t ✐s ❧✐❝❡♥s❡❞ ✉♥❞❡r t❤❡ ❈r❡❛t✐✈❡ ❈♦♠♠♦♥s ❆ttr✐❜✉t✐♦♥ ▲✐❝❡♥s❡✿ ❤tt♣✿✴✴❝r❡❛t✐✈❡❝♦♠♠♦♥s✳♦r❣✴❧✐❝❡♥s❡s✴❜②✴✶✳✵ ❚❛❜❧❡ ♦❢ ❈♦♥t❡♥ts ✶ ❙✐❣♥❛❧s ✶✳✶ ❙✐❣♥❛❧ ❈❧❛ss✐✜❝❛t✐♦♥s ❛♥❞ Pr♦♣❡rt✐❡s ✳✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶ ✶✳✷ ❙✐③❡ ♦❢ ❆ ❙✐❣♥❛❧✿ ◆♦r♠s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✾ ✶✳✸ ❙✐❣♥❛❧ ❖♣❡r❛t✐♦♥s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✾ ✶✳✹ ❯s❡❢✉❧ ❙✐❣♥❛❧s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✷✷ ✶✳✺ ❚❤❡ ■♠♣✉❧s❡ ❋✉♥❝t✐♦♥ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✷✺ ✶✳✻ ❚❤❡ ❈♦♠♣❧❡① ❊①♣♦♥❡♥t✐❛❧ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✷✽ ✶✳✼ ❉✐s❝r❡t❡✲❚✐♠❡ ❙✐❣♥❛❧s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✸✶ ❙♦❧✉t✐♦♥s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✸✺ ✷ ❙②st❡♠s ✷✳✶ ❙②st❡♠ ❈❧❛ss✐✜❝❛t✐♦♥s ❛♥❞ Pr♦♣❡rt✐❡s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✸✼ ✷✳✷ Pr♦♣❡rt✐❡s ♦❢ ❙②st❡♠s ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✹✶ ❙♦❧✉t✐♦♥s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ❄❄ ✸ ❚✐♠❡ ❉♦♠❛✐♥ ❆♥❛❧②s✐s ♦❢ ❈♦♥t✐♥✉♦✉s ❚✐♠❡ ❙②st❡♠s ✸✳✶ ❈❚ ▲✐♥❡❛r ❙②st❡♠s ❛♥❞ ❉✐✛❡r❡♥t✐❛❧ ❊q✉❛t✐♦♥s ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✹✼ ✸✳✷ ❈♦♥t✐♥✉♦✉s✲❚✐♠❡ ❈♦♥✈♦❧✉t✐♦♥ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✺✸ ✸✳✸ Pr♦♣❡rt✐❡s ♦❢ ❈♦♥✈♦❧✉t✐♦♥ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✺✾ ✸✳✹ ❇■❇❖ ❙t❛❜✐❧✐t② ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✻✺ ❙♦❧✉t✐♦♥s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ❄❄ ✹ ❚✐♠❡ ❉♦♠❛✐♥ ❆♥❛❧②s✐s ♦❢ ❉✐s❝r❡t❡ ❚✐♠❡ ❙②st❡♠s ✹✳✶ ❉✐s❝r❡t❡✲❚✐♠❡ ❙②st❡♠s ✐♥ t❤❡ ❚✐♠❡✲❉♦♠❛✐♥ ✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✻✾ ✹✳✷ ❉✐s❝r❡t❡✲❚✐♠❡ ❈♦♥✈♦❧✉t✐♦♥ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✼✷ ✹✳✸ ❈✐r❝✉❧❛r ❈♦♥✈♦❧✉t✐♦♥ ❛♥❞ t❤❡ ❉❋❚ ✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✺✼ ✹✳✹ ▲✐♥❡❛r ❈♦♥st❛♥t✲❈♦❡✣❝✐❡♥t ❉✐✛❡r❡♥❝❡ ❊q✉❛t✐♦♥s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✽✷ ✹✳✺ ❙♦❧✈✐♥❣ ▲✐♥❡❛r ❈♦♥st❛♥t✲❈♦❡✣❝✐❡♥t ❉✐✛❡r❡♥❝❡ ❊q✉❛t✐♦♥s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✽✸ ❙♦❧✉t✐♦♥s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✽✾ ✺ ▲✐♥❡❛r ❆❧❣❡❜r❛ ❖✈❡r✈✐❡✇ ✺✳✶ ▲✐♥❡❛r ❆❧❣❡❜r❛✿ ❚❤❡ ❇❛s✐❝s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✾✶ ✺✳✷ ❊✐❣❡♥✈❡❝t♦rs ❛♥❞ ❊✐❣❡♥✈❛❧✉❡s ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✾✻ ✺✳✸ ▼❛tr✐① ❉✐❛❣♦♥❛❧✐③❛t✐♦♥ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✵✶ ✺✳✹ ❊✐❣❡♥✲st✉✛ ✐♥ ❛ ◆✉ts❤❡❧❧ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳ ✶✵✹ ✺✳✺ ❊✐❣❡♥❢✉♥❝t✐♦♥s ♦❢ ▲❚■ ❙②st❡♠s ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✶✵✺ ✺✳✻ ❋♦✉r✐❡r ❚r❛♥s❢♦r♠ Pr♦♣❡rt✐❡s ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳✳✳✳✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✵✽ ❙♦❧✉t✐♦♥s ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✵✾ ✻ ❈♦♥t✐♥✉♦✉s ❚✐♠❡ ❋♦✉r✐❡r ❙❡r✐❡s ✻✳✶ P❡r✐♦❞✐❝ ❙✐❣♥❛❧s ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✶✶ ✻✳✷ ❋♦✉r✐❡r ❙❡r✐❡s✿ ❊✐❣❡♥❢✉♥❝t✐♦♥ ❆♣♣r♦❛❝❤ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✶✶✷ ✻✳✸ ❉❡r✐✈❛t✐♦♥ ♦❢ ❋♦✉r✐❡r ❈♦❡✣❝✐❡♥ts ❊q✉❛t✐♦♥ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✶✺ ✻✳✹ ❋♦✉r✐❡r ❙❡r✐❡s ✐♥ ❛ ◆✉ts❤❡❧❧ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✶✻ ✻✳✺ ❋♦✉r✐❡r ❙❡r✐❡s Pr♦♣❡rt✐❡s ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✶✾ ✻✳✻ ❙②♠♠❡tr② Pr♦♣❡rt✐❡s ♦❢ t❤❡ ❋♦✉r✐❡r ❙❡r✐❡s ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✷✷ ✻✳✼ ❈✐r❝✉❧❛r ❈♦♥✈♦❧✉t✐♦♥ Pr♦♣❡rt② ♦❢ ❋♦✉r✐❡r ❙❡r✐❡s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✶✷✻ ✻✳✽ ❋♦✉r✐❡r ❙❡r✐❡s ❛♥❞ ▲❚■ ❙②st❡♠s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳✳✳✳✳✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✷✼ ✻✳✾ ❈♦♥✈❡r❣❡♥❝❡ ♦❢ ❋♦✉r✐❡r ❙❡r✐❡s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✸✵ ✻✳✶✵ ❉✐r✐❝❤❧❡t ❈♦♥❞✐t✐♦♥s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✶✸✷ ✐✈ ✻✳✶✶ ●✐❜❜s✬s P❤❡♥♦♠❡♥❛ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✶✸✹ ✻✳✶✷ ❋♦✉r✐❡r ❙❡r✐❡s ❲r❛♣✲❯♣ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✶✸✼ ❙♦❧✉t✐♦♥s ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✸✾ ✼ ❉✐s❝r❡t❡ ❋♦✉r✐❡r ❚r❛♥s❢♦r♠ ✼✳✶ ❋♦✉r✐❡r ❆♥❛❧②s✐s ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✹✶ ✼✳✷ ❋♦✉r✐❡r ❆♥❛❧②s✐s ✐♥ ❈♦♠♣❧❡① ❙♣❛❝❡s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✹✷ ✼✳✸ ▼❛tr✐① ❊q✉❛t✐♦♥ ❢♦r t❤❡ ❉❚❋❙ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✶✹✽ ✼✳✹ P❡r✐♦❞✐❝ ❊①t❡♥s✐♦♥ t♦ ❉❚❋❙ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✺✵ ✼✳✺ ❈✐r❝✉❧❛r ❙❤✐❢ts ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✶✺✸ ✼✳✻ ❈✐r❝✉❧❛r ❈♦♥✈♦❧✉t✐♦♥ ❛♥❞ t❤❡ ❉❋❚ ✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✺✼ ❙♦❧✉t✐♦♥s ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✻✷ ✽ ❋❛st ❋♦✉r✐❡r ❚r❛♥s❢♦r♠ ✭❋❋❚✮ ✽✳✶ ❉❋❚✿ ❋❛st ❋♦✉r✐❡r ❚r❛♥s❢♦r♠ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✻✸ ✽✳✷ ❚❤❡ ❋❛st ❋♦✉r✐❡r ❚r❛♥s❢♦r♠ ✭❋❋❚✮ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✶✻✹ ✽✳✸ ❉❡r✐✈✐♥❣ t❤❡ ❋❛st ❋♦✉r✐❡r ❚r❛♥s❢♦r♠ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✻✺ ❙♦❧✉t✐♦♥s ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✻✽ ✾ ❈♦♥✈❡r❣❡♥❝❡ ✾✳✶ ❈♦♥✈❡r❣❡♥❝❡ ♦❢ ❙❡q✉❡♥❝❡s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✻✾ ✾✳✷ ❈♦♥✈❡r❣❡♥❝❡ ♦❢ ❱❡❝t♦rs ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✼✶ ✾✳✸ ❯♥✐❢♦r♠ ❈♦♥✈❡r❣❡♥❝❡ ♦❢ ❋✉♥❝t✐♦♥ ❙❡q✉❡♥❝❡s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✼✹ ❙♦❧✉t✐♦♥s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ❄❄ ✶✵ ❉✐s❝r❡t❡ ❚✐♠❡ ❋♦✉r✐❡r ❚r❛♥s❢♦r♠ ✭❉❚❋❚✮ ✶✵✳✶ ❉✐s❝r❡t❡ ❋♦✉r✐❡r ❚r❛♥s❢♦r♠❛t✐♦♥ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✼✼ ✶✵✳✷ ❉✐s❝r❡t❡ ❋♦✉r✐❡r ❚r❛♥s❢♦r♠ ✭❉❋❚✮ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳✳✳✳✳✳✳✳ ✶✼✾ ✶✵✳✸ ❚❛❜❧❡ ♦❢ ❈♦♠♠♦♥ ❋♦✉r✐❡r ❚r❛♥s❢♦r♠s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✽✶ ✶✵✳✹ ❉✐s❝r❡t❡✲❚✐♠❡ ❋♦✉r✐❡r ❚r❛♥s❢♦r♠ ✭❉❚❋❚✮ ✳ ✳✳✳✳✳✳✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✽✷ ✶✵✳✺ ❉✐s❝r❡t❡✲❚✐♠❡ ❋♦✉r✐❡r ❚r❛♥s❢♦r♠ Pr♦♣❡rt✐❡s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✽✸ ✶✵✳✻ ❉✐s❝r❡t❡✲❚✐♠❡ ❋♦✉r✐❡r ❚r❛♥s❢♦r♠ P❛✐r ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳✳✳✳✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✽✸ ✶✵✳✼ ❉❚❋❚ ❊①❛♠♣❧❡s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✽✹ ❙♦❧✉t✐♦♥s ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✽✽ ✶✶ ❈♦♥t✐♥✉♦✉s ❚✐♠❡ ❋♦✉r✐❡r ❚r❛♥s❢♦r♠ ✭❈❚❋❚✮ ✶✶✳✶ ❈♦♥t✐♥✉♦✉s✲❚✐♠❡ ❋♦✉r✐❡r ❚r❛♥s❢♦r♠ ✭❈❚❋❚✮ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✶✽✾ ✶✶✳✷ Pr♦♣❡rt✐❡s ♦❢ t❤❡ ❈♦♥t✐♥✉♦✉s✲❚✐♠❡ ❋♦✉r✐❡r ❚r❛♥s❢♦r♠ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✾✵ ❙♦❧✉t✐♦♥s ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✾✹ ✶✷ ❙❛♠♣❧✐♥❣ ❚❤❡♦r❡♠ ✶✷✳✶ ❙❛♠♣❧✐♥❣ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✶✾✺ ✶✷✳✷ ❘❡❝♦♥str✉❝t✐♦♥ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✶✾✾ ✶✷✳✸ ▼♦r❡ ♦♥ ❘❡❝♦♥str✉❝t✐♦♥ ✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳ ✷✵✸ ✶✷✳✹ ◆②q✉✐st ❚❤❡♦r❡♠ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✷✵✺ ✶✷✳✺ ❆❧✐❛s✐♥❣ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✷✵✻ ✶✷✳✻ ❆♥t✐✲❆❧✐❛s✐♥❣ ❋✐❧t❡rs ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✷✶✵ ✶✷✳✼ ❉✐s❝r❡t❡ ❚✐♠❡ Pr♦❝❡ss✐♥❣ ♦❢ ❈♦♥t✐♥✉♦✉s ❚✐♠❡ ❙✐❣♥❛❧s ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✷✶✶ ❙♦❧✉t✐♦♥s ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✷✶✹ ✶✸ ▲❛♣❧❛❝❡ ❚r❛♥s❢♦r♠ ❛♥❞ ❙②st❡♠ ❉❡s✐❣♥ ✶✸✳✶ ❚❤❡ ▲❛♣❧❛❝❡ ❚r❛♥s❢♦r♠s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✷✶✼ ✶✸✳✷ Pr♦♣❡rt✐❡s ♦❢ t❤❡ ▲❛♣❧❛❝❡ ❚r❛♥s❢♦r♠ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✷✶✾ ✶✸✳✸ ❚❛❜❧❡ ♦❢ ❈♦♠♠♦♥ ▲❛♣❧❛❝❡ ❚r❛♥s❢♦r♠s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✷✷✶ ✶✸✳✹ ❘❡❣✐♦♥ ♦❢ ❈♦♥✈❡r❣❡♥❝❡ ❢♦r t❤❡ ▲❛♣❧❛❝❡ ❚r❛♥s❢♦r♠ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✷✷✶ ✈ ✶✸✳✺ ❚❤❡ ■♥✈❡rs❡ ▲❛♣❧❛❝❡ ❚r❛♥s❢♦r♠ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✷✷✸ ✶✸✳✻ P♦❧❡s ❛♥❞ ❩❡r♦s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✷✷✺ ❙♦❧✉t✐♦♥s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ❄❄ ✶✹ ❩✲❚r❛♥s❢♦r♠ ❛♥❞ ❉✐❣✐t❛❧ ❋✐❧t❡r✐♥❣ ✶✹✳✶ ❚❤❡ ❩ ❚r❛♥s❢♦r♠✿ ❉❡✜♥✐t✐♦♥ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✷✷✾ ✶✹✳✷ ❚❛❜❧❡ ♦❢ ❈♦♠♠♦♥ ③✲❚r❛♥s❢♦r♠s ✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✷✸✹ ✶✹✳✸ ❘❡❣✐♦♥ ♦❢ ❈♦♥✈❡r❣❡♥❝❡ ❢♦r t❤❡ ❩✲tr❛♥s❢♦r♠ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✷✸✺ ✶✹✳✹ ■♥✈❡rs❡ ❩✲❚r❛♥s❢♦r♠ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✷✹✹ ✶✹✳✺ ❘❛t✐♦♥❛❧ ❋✉♥❝t✐♦♥s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✷✹✼ ✶✹✳✻ ❉✐✛❡r❡♥❝❡ ❊q✉❛t✐♦♥ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✷✹✾ ✶✹✳✼ ❯♥❞❡rst❛♥❞✐♥❣ P♦❧❡✴❩❡r♦ P❧♦ts ♦♥ t❤❡ ❩✲P❧❛♥❡ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✷✺✷ ✶✹✳✽ ❋✐❧t❡r ❉❡s✐❣♥ ✉s✐♥❣ t❤❡ P♦❧❡✴❩❡r♦ P❧♦t ♦❢ ❛ ❩✲❚r❛♥s❢♦r♠ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✷✺✻ ❙♦❧✉t✐♦♥s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ❄❄ ✶✺ ❆♣♣❡♥❞✐①✿ ❍✐❧❜❡rt ❙♣❛❝❡s ❛♥❞ ❖rt❤♦❣♦♥❛❧ ❊①♣❛♥s✐♦♥s ✶✺✳✶ ❱❡❝t♦r ❙♣❛❝❡s ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✷✻✶ ✶✺✳✷ ◆♦r♠s ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✷✻✸ ✶✺✳✸ ■♥♥❡r Pr♦❞✉❝ts ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✷✻✻ ✶✺✳✹ ❍✐❧❜❡rt ❙♣❛❝❡s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✷✻✽ ✶✺✳✺ ❈❛✉❝❤②✲❙❝❤✇❛r③ ■♥❡q✉❛❧✐t② ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✷✻✽ ✶✺✳✻ ❈♦♠♠♦♥ ❍✐❧❜❡rt ❙♣❛❝❡s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✷✼✺ ✶✺✳✼ ❚②♣❡s ♦❢ ❇❛s✐s ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✷✼✽ ✶✺✳✽ ❖rt❤♦♥♦r♠❛❧ ❇❛s✐s ❊①♣❛♥s✐♦♥s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✷✽✶ ✶✺✳✾ ❋✉♥❝t✐♦♥ ❙♣❛❝❡ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✷✽✺ ✶✺✳✶✵ ❍❛❛r ❲❛✈❡❧❡t ❇❛s✐s ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✷✽✻ ✶✺✳✶✶ ❖rt❤♦♥♦r♠❛❧ ❇❛s❡s ✐♥ ❘❡❛❧ ❛♥❞ ❈♦♠♣❧❡① ❙♣❛❝❡s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✷✾✸ ✶✺✳✶✷ P❧❛♥❝❤❛r❡❧ ❛♥❞ P❛rs❡✈❛❧✬s ❚❤❡♦r❡♠s ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳ ✷✾✺ ✶✺✳✶✸ ❆♣♣r♦①✐♠❛t✐♦♥ ❛♥❞ Pr♦❥❡❝t✐♦♥s ✐♥ ❍✐❧❜❡rt ❙♣❛❝❡ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✷✾✻ ❙♦❧✉t✐♦♥s ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✷✾✾ ✶✻ ❍♦♠❡✇♦r❦ ❙❡ts ✶✻✳✶ ❍♦♠❡✇♦r❦ ✶ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✸✵✶ ✶✻✳✷ ❍♦♠❡✇♦r❦ ✶ ❙♦❧✉t✐♦♥s ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✸✵✺ ❙♦❧✉t✐♦♥s ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ❄❄ ✶✼ ❱✐❡✇✐♥❣ ❊♠❜❡❞❞❡❞ ▲❛❜❱■❊❲ ❈♦♥t❡♥t ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✸✶✼ ●❧♦ss❛r② ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳✳✳✳✳✳✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✸✶✽ ■♥❞❡① ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✸✷✸ ❆ttr✐❜✉t✐♦♥s ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✳ ✳✸✷✽ ✈✐ ❈❤❛♣t❡r ✶ ❙✐❣♥❛❧s ✶✳✶ ❙✐❣♥❛❧ ❈❧❛ss✐✜❝❛t✐♦♥s ❛♥❞ Pr♦♣❡rt✐❡s ✶ ✶✳✶✳✶ ■♥tr♦❞✉❝t✐♦♥ ❚❤✐s ♠♦❞✉❧❡ ✇✐❧❧ ❧❛② ♦✉t s♦♠❡ ♦❢ t❤❡ ❢✉♥❞❛♠❡♥t❛❧s ♦❢ s✐❣♥❛❧ ❝❧❛ss✐✜❝❛t✐♦♥✳ ❚❤✐s ✐s ❜❛s✐❝❛❧❧② ❛ ❧✐st ♦❢ ❞❡✜♥✐t✐♦♥s ❛♥❞ ♣r♦♣❡rt✐❡s t❤❛t ❛r❡ ❢✉♥❞❛♠❡♥t❛❧ t♦ t❤❡ ❞✐s❝✉ss✐♦♥ ♦❢ s✐❣♥❛❧s ❛♥❞ s②st❡♠s✳ ■t s❤♦✉❧❞ ❜❡ ♥♦t❡❞ t❤❛t s♦♠❡ ❞✐s❝✉ss✐♦♥s ❧✐❦❡ ❡♥❡r❣② s✐❣♥❛❧s ✈s✳ ♣♦✇❡r s✐❣♥❛❧s ✷ ❤❛✈❡ ❜❡❡♥ ❞❡s✐❣♥❛t❡❞ t❤❡✐r ♦✇♥ ♠♦❞✉❧❡ ❢♦r ❛ ♠♦r❡ ❝♦♠♣❧❡t❡ ❞✐s❝✉ss✐♦♥✱ ❛♥❞ ✇✐❧❧ ♥♦t ❜❡ ✐♥❝❧✉❞❡❞ ❤❡r❡✳ ✶✳✶✳✷ ❈❧❛ss✐✜❝❛t✐♦♥s ♦❢ ❙✐❣♥❛❧s ❆❧♦♥❣ ✇✐t❤ t❤❡ ❝❧❛ss✐✜❝❛t✐♦♥ ♦❢ s✐❣♥❛❧s ❜❡❧♦✇✱ ✐t ✐s ❛❧s♦ ✐♠♣♦rt❛♥t t♦ ✉♥❞❡rst❛♥❞ t❤❡ ❈❧❛ss✐✜❝❛t✐♦♥ ♦❢ ❙②st❡♠s ✭❙❡❝t✐♦♥ ✷✳✶✮✳ ✶✳✶✳✷✳✶ ❈♦♥t✐♥✉♦✉s✲❚✐♠❡ ✈s✳ ❉✐s❝r❡t❡✲❚✐♠❡ ❆s t❤❡ ♥❛♠❡s s✉❣❣❡st✱ t❤✐s ❝❧❛ss✐✜❝❛t✐♦♥ ✐s ❞❡t❡r♠✐♥❡❞ ❜② ✇❤❡t❤❡r ♦r ♥♦t t❤❡ t✐♠❡ ❛①✐s ✭①✲❛①✐s✮ ✐s ❞✐s❝r❡t❡ ✭❝♦✉♥t❛❜❧❡✮ ♦r ❝♦♥t✐♥✉♦✉s ✭❋✐❣✉r❡ ✶✳✶✮✳ ❆ ❝♦♥t✐♥✉♦✉s✲t✐♠❡ s✐❣♥❛❧ ✇✐❧❧ ❝♦♥t❛✐♥ ❛ ✈❛❧✉❡ ❢♦r ❛❧❧ r❡❛❧ ♥✉♠❜❡rs ❛❧♦♥❣ t❤❡ t✐♠❡ ❛①✐s✳ ■♥ ❝♦♥tr❛st t♦ t❤✐s✱ ❛ ❞✐s❝r❡t❡✲t✐♠❡ s✐❣♥❛❧ ✭❙❡❝t✐♦♥ ✶✳✼✮ ✐s ♦❢t❡♥ ❝r❡❛t❡❞ ❜② ✉s✐♥❣ t❤❡ s❛♠♣❧✐♥❣ t❤❡♦r❡♠ ✸ t♦ s❛♠♣❧❡ ❛ ❝♦♥t✐♥✉♦✉s s✐❣♥❛❧✱ s♦ ✐t ✇✐❧❧ ♦♥❧② ❤❛✈❡ ✈❛❧✉❡s ❛t ❡q✉❛❧❧② s♣❛❝❡❞ ✐♥t❡r✈❛❧s ❛❧♦♥❣ t❤❡ t✐♠❡ ❛①✐s✳ ✶ ❚❤✐s ❝♦♥t❡♥t ✐s ❛✈❛✐❧❛❜❧❡ ♦♥❧✐♥❡ ❛t ❁❤tt♣✿✴✴❝♥①✳♦r❣✴❝♦♥t❡♥t✴♠✶✵✵✺✼✴✷✳✶✼✴❃✳ ✷ ✧❙✐❣♥❛❧ ❊♥❡r❣② ✈s✳ ❙✐❣♥❛❧ P♦✇❡r✧ ❁❤tt♣✿✴✴❝♥①✳♦r❣✴❝♦♥t❡♥t✴♠✶✵✵✺✺✴❧❛t❡st✴❃ ✸ ✧❚❤❡ ❙❛♠♣❧✐♥❣ ❚❤❡♦r❡♠✧ ❁❤tt♣✿✴✴❝♥①✳♦r❣✴❝♦♥t❡♥t✴♠✵✵✺✵✴❧❛t❡st✴❃ ✶ ✷ ❈❍❆P❚❊❘ ✶✳ ❙■●◆❆▲❙ ❋✐❣✉r❡ ✶✳✶ ✶✳✶✳✷✳✷ ❆♥❛❧♦❣ ✈s✳ ❉✐❣✐t❛❧ ❚❤❡ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ ❛♥❛❧♦❣ ❛♥❞ ❞✐❣✐t❛❧ ✐s s✐♠✐❧❛r t♦ t❤❡ ❞✐✛❡r❡♥❝❡ ❜❡t✇❡❡♥ ❝♦♥t✐♥✉♦✉s✲t✐♠❡ ❛♥❞ ❞✐s❝r❡t❡✲ t✐♠❡✳ ■♥ t❤✐s ❝❛s❡✱ ❤♦✇❡✈❡r✱ t❤❡ ❞✐✛❡r❡♥❝❡ ✐s ✇✐t❤ r❡s♣❡❝t t♦ t❤❡ ✈❛❧✉❡ ♦❢ t❤❡ ❢✉♥❝t✐♦♥ ✭②✲❛①✐s✮ ✭❋✐❣✉r❡ ✶✳✷✮✳ ❆♥❛❧♦❣ ❝♦rr❡s♣♦♥❞s t♦ ❛ ❝♦♥t✐♥✉♦✉s ②✲❛①✐s✱ ✇❤✐❧❡ ❞✐❣✐t❛❧ ❝♦rr❡s♣♦♥❞s t♦ ❛ ❞✐s❝r❡t❡ ②✲❛①✐s✳ ❆♥ ❡❛s② ❡①❛♠♣❧❡ ♦❢ ❛ ❞✐❣✐t❛❧ s✐❣♥❛❧ ✐s ❛ ❜✐♥❛r② s❡q✉❡♥❝❡✱ ✇❤❡r❡ t❤❡ ✈❛❧✉❡s ♦❢ t❤❡ ❢✉♥❝t✐♦♥ ❝❛♥ ♦♥❧② ❜❡ ♦♥❡ ♦r ③❡r♦✳ ❋✐❣✉r❡ ✶✳✷ ✶✳✶✳✷✳✸ P❡r✐♦❞✐❝ ✈s✳ ❆♣❡r✐♦❞✐❝ P❡r✐♦❞✐❝ s✐❣♥❛❧s ✭❙❡❝t✐♦♥ ✻✳✶✮ r❡♣❡❛t ✇✐t❤ s♦♠❡ ♣❡r✐♦❞ T✱ ✇❤✐❧❡ ❛♣❡r✐♦❞✐❝✱ ♦r ♥♦♥♣❡r✐♦❞✐❝✱ s✐❣♥❛❧s ❞♦ ♥♦t ✭❋✐❣✉r❡ ✶✳✸✮✳ ❲❡ ❝❛♥ ❞❡✜♥❡ ❛ ♣❡r✐♦❞✐❝ ❢✉♥❝t✐♦♥ t❤r♦✉❣❤ t❤❡ ❢♦❧❧♦✇✐♥❣ ♠❛t❤❡♠❛t✐❝❛❧ ❡①♣r❡ss✐♦♥✱ ✇❤❡r❡ t ❝❛♥ ❜❡ ❛♥② ♥✉♠❜❡r ❛♥❞ T ✐s ❛ ♣♦s✐t✐✈❡ ❝♦♥st❛♥t✿ f (t) = f (T + t) ✭✶✳✶✮ ❚❤❡ ❢✉♥❞❛♠❡♥t❛❧ ♣❡r✐♦❞ ♦❢ ♦✉r ❢✉♥❝t✐♦♥✱ f (t)✱ ✐s t❤❡ s♠❛❧❧❡st ✈❛❧✉❡ ♦❢ T t❤❛t t❤❡ st✐❧❧ ❛❧❧♦✇s ✭✶✳✶✮ t♦ ❜❡ tr✉❡✳ [...]... accurately predicted and can usually 5 only be guessed based on the averages of sets of signals (Figure 1.7) (a) (b) Figure 1.7: (a) Deterministic Signal (b) Random Signal 1.1.2.7 Right-Handed vs Left-Handed A right-handed signal and left-handed signal are those signals whose value is zero between a given variable and positive or negative innity Mathematically speaking, a right-handed signal is dened... signal f (t) = 0 for t < t1 < ∞, and a left-handed signal t > t1 > −∞ See (Figure 1.8) for an example Both gures where is dened as any signal where "begin" at t1 f (t) = 0 for and then extends to positive or negative innity with mainly nonzero values 4 "Introduction to Random Signals and Processes" 5 "Random Processes: Mean and Variance" ... ) SIGNALS 17 Figure 1.22 1 compute 2 look at Pf Energy T lim T →∞ = Energy T ( 2 f 2) T 2 ( f 2) = T is often called the mean-square value of f Pf is called the root mean squared (RMS) value of f Units? "Energy signals" have nite norm (energy) Ef < ∞ Pf < ∞, Pf = 0, "Power signals" have nite and nonzero power 1.2.5.1 Conclusions Energy signals are not power signals Power signals are not energy signals. .. period T0 (b) An aperiodic signal 1.1.2.4 Causal vs Anticausal vs Noncausal Causal signals are signals that are zero for all negative time, while anticausal are signals that are zero for all positive time Noncausal signals are signals that have nonzero values in both positive and negative time (Figure 1.4) CHAPTER 1 4 SIGNALS (a) (b) (c) Figure 1.4: (a) A causal signal (b) An anticausal signal (c) A... Variance" CHAPTER 1 8 SIGNALS (a) (b) Figure 1.8: (a) Right-handed signal (b) Left-handed signal 1.1.2.8 Finite vs Innite Length As the name applies, signals can be characterized as to whether they have a nite or innite length set of values Most nite length signals are used when dealing with discrete-time signals or a given sequence of values Mathematically speaking,... are not energy signals Why? Exercise 1.5 Are all signals either energy or power signals? Example 1.9 f (t) = t and ( → Ef = ∞) CHAPTER 1 18 SIGNALS Figure 1.23 The 4 fundamental classes of signals we will study depend on the independent (time) variable 19 Figure 1.24 1.3 Signal Operations 7 This module will look at two signal operations, time shifting and time scaling Signal operations are operations... operations are operations on the time variable of the signal These operations are very common components to real-world systems and, as such, should be understood thoroughly when learning about signals and systems 7 This content is available online at CHAPTER 1 20 SIGNALS 1.3.1 Time Shifting Time shifting is, as the name suggests, the shifting of a signal in time This is... of the most fundamental and important signal in signal and system Its importance comes from its functions as a basis for periodic signals as well as being able to characterize linear, time-invariant (Section 2.1) signals Before proceeding, you should be familiar with the ideas and functions of complex numbers 13 1.6.1.1 Basic Exponential For all numbers x, we easily derive and dene the ex = 1 + exponential... 1.1.2.6 Deterministic vs Random A deterministic signal is a signal in which each value of the signal is xed and can be determined by a mathematical expression, rule, or table Because of this the future values of the signal can be calculated from past values with complete condence On the other hand, a random signal 4 has a lot of uncertainty about its behavior The future values of a random signal cannot... of a sequence or any number of things in any number of dimensions Most, if not all, signals that you will encounter in your studies and the real world will be able to be created from the basic signals we discuss below Because of this, these elementary signals are often referred to as the building blocks for all other signals 1.4.1 Sinusoids Probably the most important elemental signal that you will . Signals and Systems Collection Editor: Richard Baraniuk Signals and Systems Collection Editor: Richard Baraniuk Authors: Thanos Antoulas Richard Baraniuk