Filter design and equalization - MIT OpenCourseWare

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FIR filtersfinite impulse response (FIR) filter:n−1y(t) = h τ u(t − τ),τ=0t ∈ Z• (sequence) u : Z →• (sequence) y : Z →R is input signalR is output signal• h i are called filter coefficients• n is filter order or length<strong>Filter</strong> <strong>design</strong> 2
Page 4: example: (lowpass) FIR filter, orde
Page 7 and 8: Chebychev design via SOCP:minimizes
Page 9 and 10: • term e −iNω represents N-sam
Page 11 and 12: specifications:• maximum passband
Page 13 and 14: • passband ripple δ 1 is given
Page 15 and 16: frequency response magnitude (i.e.,
Page 17 and 18: Chebychev equalizer design:minimize
Page 19 and 20: extensions:• can impose (convex)
Page 21 and 22: 110 G(ω) |G(ω)|010−1100 0.5 1 1
Page 23 and 24: equalized frequency response magnit
Page 25 and 26: equalized frequency response magnit
Page 27 and 28: Autocorrelation coefficientsautocor
Page 29 and 30: Spectral factorizationquestion: whe
Page 31 and 32: example: 1/f (pink noise) filter (i

Filter design and equalization - MIT OpenCourseWare

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