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Unformatted text preview: and communications 12.1 FIR low-pass ﬁlter design. Consider the (symmetric, linear phase) ﬁnite impulse response (FIR)
ﬁlter described by its frequency response
N ak cos kω, H (ω ) = a 0 +
k=1 where ω ∈ [0, π ] is the frequency. The design variables in our problems are the real coeﬃcients
a = (a0 , . . . , aN ) ∈ RN +1 , where N is called the order or length of the FIR ﬁlter. In this problem
we will explore the design of a low-pass lter, with speciﬁcations:
• For 0 ≤ ω ≤ π/3, 0.89 ≤ H (ω ) ≤ 1.12, i.e., the ﬁlter has about ±1dB ripple in the ‘passband’
• For ωc ≤ ω ≤ π , |H (ω )| ≤ α. In other words, the ﬁlter achieves an attenuation given by α in
the ‘stopband’ [ωc , π ]. Here ωc is called the ﬁlter ‘cutoﬀ frequency’.
(It is called a low-pass ﬁlter since low frequencies are allowed to pass, but frequencies above the
cutoﬀ frequency are attenuated.) These speciﬁcations are depicted graphically in the ﬁgure below. H (ω ) 1.12
−α0 π/3 ωc ω π For parts (a)–(c), explain how to formulate the given problem as a convex o...
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This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at University of California, Berkeley.
- Fall '13
- The Aeneid