Filter design and equalization - MIT OpenCourseWare

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choose h to minimizelog-Chebychev magnitude designmax | 20 log 10 | H(ω) | − 20 log 10 D(ω) |ω• D is desired transfer function magnitude(D(ω) > 0 for all ω)• find minimax logarithmic (dB) fitreformulate asminimize tsubject to D(ω) 2 /t ≤ R(ω) ≤ tD(ω) 2 ,0 ≤ ω ≤ π• convex in variables r, t• constraint includes spectral factorization conditionFilter design 30
example: 1/f (pink noise) filter (i.e., D(ω) = 1/ √ ω), n = 50,log-Chebychev design over 0.01π ≤ ω ≤ π1100102|H(ω)|−110−210−1 010 10ωoptimal fit: ±0.5dBFilter design 31
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 12 and 13: Linear phase lowpass filter design
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 32: MIT OpenCourseWarehttp://ocw.mit.ed

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