Filter design and equalization - MIT OpenCourseWare

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time-domain equalization: optimize impulse response g˜ of equalizedsysteme.g., with G des (ω) = e −iDω ,g des (t) =1 t = D0 t = Dsample design:minimize max t =D | g˜(t) |subject to g˜(D) = 1• an LP• can useg˜(t) 2 ort=D t =D|g˜(t)|Filter design 18
extensions:• can impose (convex) constraints• can mix time- and frequency-domain specifications• can equalize multiple systems, i.e., choose H soG (k) H ≈ G des ,k = 1, ...,K• can equalize multi-input multi-output systems(i.e., G and H are matrices)• extends to multidimensional systems, e.g., image processingFilter design 19
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 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

Filter design and equalization - MIT OpenCourseWare

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