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עמוד:*26
Filtering differentiators The following filter / observer is build on the basis of the standard differentiator ( 4 ) and is capable of filtering out some unbounded sampling noises . Introduce the number n f ≥ 0 which is further called the filtering order . Correspond - ingly, n d is further called the differentiation order . Let n = n d + n f , the filtering differ - entiator is defined by the following form w 1 = − ˜ λ n d + n f L 1 ˙ nd + nf + 1 w 1 � nd + nf � nd + nf + 1 w 2 , + . . . w n f − 1 = − ˜ λ n d + 2 L nf − 1 ˙ nd + nf + 1 w 1 � n + 2 � n + nf + 1 w n f , + w n f = − ˜ λ n d + 1 L nf ˙ nd + nf + 1 w 1 � nd + 1 � nd + nf + 1 w n f + 1 , + w n f + 1 = z 0 − f ( t ) , ) 9 ( z 0 = − ˜ λ n d L nf + 1 ˙ nd + nf + 1 w 1 � nd � nd + nf + 1 z 1 , + . . . z n d − 1 = − ˜ λ 1 L nd + nf ˙ nd + nf + 1 w 1 � 1 � nd + nf + 1 z n d , + z ˙ n d = − ˜ λ 0 Lsign ( w 1 ) , | f ( n d + 1 ) L . ≤ | 0 ) 10 ( For n f = 0 the fictitious variable w n f + 1 turns into w 1 , DEs of ( 9 ) disappear and ( 10 ) turns into the standard differentiator ( 4 ) . The assumptions on the input signal are the same . Denote ζ i = w i + 1 / Lfor i = 0 , . . . , n f − 1 , and ζ i + n f = ( z i − f ( i ) Lfor i = 0 , . . . , n d . / ) 0 Now subtracting f ( k + 1 ) from the both sides of the equation for z k in ( 10 ) , k = 0 , . . . , n d , 0 dividing ( 9 ) and ( 10 ) by L, and taking into account f ( n d + 1 ) L∈ [ − 1 , 1 ] obtain the FT / 0 * 26
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אדמוני, אריאל
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