Filter design and equalization - MIT OpenCourseWare

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Linear phase lowpass filter design• sample frequency• can assume wlog H (0) > 0, so ripple spec is1/δ 1 ≤ H(ω k ) ≤ δ 1design for maximum stopband attenuation:minimize δ 2subject to 1/δ 1 ≤ H(ω k ) ≤ δ 1 ,−δ 2 ≤ H(ω k ) ≤ δ 2 ,0 ≤ ω k ≤ ω pω s ≤ ω k ≤ πFilter design 12
• passband ripple δ 1 is given• an LP in variables h, δ 2• known (and used) since 1960’s• can add other constraints, e.g., |h i | ≤ αvariations and extensions:• fix δ 2 , minimize δ 1 (convex, but not LP)• fix δ 1 and δ 2 , minimize ω s (quasiconvex)• fix δ 1 and δ 2 , minimize order n (quasiconvex)Filter design 13
Page 2: FIR filtersfinite impulse response
Page 6 and 7: • h is optimization variableCheby
Page 8 and 9: Linear phase filterssuppose• n =
Page 10 and 11: Lowpass filter specificationsδ 11/
Page 14 and 15: example• linear phase filter, n =
Page 16 and 17: Equalizer designH(ω)G(ω)equalizat
Page 18 and 19: time-domain equalization: optimize
Page 20 and 21: Equalizer design exampleunequalized
Page 22 and 23: Chebychev equalizer design:minimize
Page 24 and 25: time-domain equalizer design:equali
Page 26 and 27: Filter magnitude specificationstran
Page 28 and 29: Fourier transform of autocorrelatio
Page 30 and 31: choose h to minimizelog-Chebychev m
Page 32: MIT OpenCourseWarehttp://ocw.mit.ed

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