Filter design and equalization - MIT OpenCourseWare

More documents

Recommendations

Info

Filter magnitude specificationstransfer function magnitude spec has formL(ω) ≤ |H(ω)| ≤ U(ω),ω ∈ [0,π]where L, U : R→R + are given• lower bound is not convex in filter coefficients h• arises in many applications, e.g., audio, spectrum shaping• can change variables to solve via convex optimizationFilter design 26
Autocorrelation coefficientsautocorrelation coefficients associated with impulse responseh = (h 0 ,...,h n−1 ) ∈ R n arer t = h τ h τ+tτ(we take h k = 0 for k < 0 or k ≥ n)• r t = r −t ; r t = 0 for |t| ≥ n• hence suffices to specify r = (r 0 , . ..,r n−1 ) ∈ R nFilter design 27
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 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

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?