Rügen voorjaar 2013 Verslag van het KNNV-kamp op Rügen van 4 - 12 mei 2013

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Il tempo non e’ variabile continua: esiste soltanto una successione di istanti di tempo multipli interi di un intervallo di tempo fissato, chiamato periodo di campionamento.

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y [t k ] 2 R

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d [t k ] 2 R

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• Per semplicità in ciò che segue trascuriamo di indicare esplicitamente l’intervallo di campionamento

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Si tratta di sistemi ibridi in cui convivono variabili a tempo continuo ed a tempo discreto

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e [k]

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Segnale continuo, analogico

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e [k]

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e [k]

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u [k]

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• segnali digitali: le loro ampiezze sono quantizzate

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in tutte le situazioni di interesse

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y [k] ' w [k]

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e [k] = w [k] y [k]

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Uscita desiderata:

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?

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ammortizzatore non hanno effetti trascurabili

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Per semplicità supponiamo che il riferimento h 0 (t) sia scalino unitario e condizioni iniziali nulle.

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ˆ u [k]

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e [k] = e (t k ) , ˆ u [k] = µ ˆ e [k] , u(t) = ˆ u [k] , kT  t < (k + 1)T

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u [0] = µ ˆ e [0] = µ

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… e così via …

<latexit sha1_base64="jW7UZOiFOatHrtUt46Q9GWWQpBA=">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</latexit>

e [1] = e(T ) = w(T ) y(T ) = 1 µT

<latexit sha1_base64="YfC7fL/MrhjekXLNiH1kdGrAUpQ=">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</latexit>

e [2] = e(2T ) = w(2T ) y(2T ) = (1 µT ) 2

<latexit sha1_base64="kID7oFRybXnJzBK1toqaRr+rqww=">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</latexit>

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Si confronti questo risultato con quello di slide # 54, 58 e 60 !

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y [k] = 1 (1 µT ) k , k 0

<latexit sha1_base64="t47reApYg4HcNdJxdM0vBPh1kDQ=">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</latexit>

k lim !1 y [k] = 1 ˆ

<latexit sha1_base64="xSCH4BGh0PUsUT2lslN5BF7qS8Q=">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</latexit>

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