recitation3 notes

recitation3 notes - Filtering 1 14.384 Time Series Analysis...

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Filtering 1 14.384 Time Series Analysis, Fall 2007 Recitation by Paul Schrimpf Supplementary to lectures given by Anna Mikusheva September 21, 2007 Recitation 3 Filtering In lecture 4, we introduced filtering. Here we’ll spend a bit more time deriving some common filters and showing how to use them. Recall that an ideal band-pass filter has B ( e i� ) = 1 [ ω l , ω h ] 0 otherwise and can be written as B ( e i� ) = j e i�j −∈ where 1 = e i�j d� j 2 ω | |� [ l ,� h ] 1 = e i�j d� + e i�j d� 2 ω l ,� h h , l 1 = e i� h j e i� l j + e i� l j e i� h j 2 ωij sin( j� h ) sin( j� l ) j = 0 = �j h l j = 0 Baxter-King Baxter and King (1999) proposed approximating the ideal filter with one of order J by solving 1 i� B ( e i� ) | 2 min | B ( e d� B () 2 ω s.t. B (1) = β
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Baxter-King 2 where the constraint may or may not be present.
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