Explain in detail how to solve this problem using

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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’ [0, π/3]. • 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 1.00 0.89 α 0 −α0 π/3 ωc ω π For parts (a)–(c), explain how to formulate the given problem as a convex o...
View Full Document

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.

Ask a homework question - tutors are online