recitation3 notes

J christiano fitzgerald 3 christiano fitzgerald

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Unformatted text preview: j − β |j |�J Using the fact that conditions for bj are 1 2� �� ei�(j −k) = −� ⎛ 1 j=k and 0 j=k � � bj = � j + 1 2� �� −� � B � (� )ei�j = �j , the first order � 2 Using the constraint to solve for � gives: β= � � �j + |j |�J �= ⎤ 2J + 1 � 2 2� β− 2J + 1 � |j |�J � � �j ⎞ To summarize: the Baxter King filter of order J on [ωl , ωh ] constrained to have B (0) = β is given by � bj =�j + λ where � �j = λ= ⎛ sin(j�h )−sin(j�l ) �j �h −�l � ⎤ j �=...
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