Download This File - The Free Information Society

More documents

Recommendations

Info

opt = V H V −1 V H h ∞ (|hd (n) − h (n) |) 2 mina,b n=0 ⎧ ⎛ ⎨ ∞ M minα,β ⎝ |hd (n) − αie ⎩ βin 2 | ⎞⎫ ⎬ ⎠ ⎭ n=0 αi βi ⎛ ⎜ ⎝ hd (0) 0 ... 0 hd (1) hd (0) ... 0 i=1 hd (N − 1) hd (N − 2) ... hd (N − M) ⎞ ⎛ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎠ ⎝ a1 a2 aM ⎞ ⎛ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ≈ − ⎜ ⎟ ⎜ ⎠ ⎝ hd (1) hd (2) hd (N) a = Hd H −1 Hd Hd H hd Hd H Hd = R rij hd rij = N−max{ i,j } k=0 Hd H hd = rd (i) = N−i n=0 (hd (k) hd (k + |i − j|)) ⎛ ⎜ ⎝ rd (1) rd (2) rd (3) rd (M) ⎞ ⎟ ⎠ (hd (n) hd (n + i)) aopt = − RH rd Ra = −r R M × M a M × 1 r M × 1 ⎞ ⎟ ⎠
ij ≈ r (i − j) = r (j − i) rij = r (i − j) ⎛ ⎜ ⎝ ⎞ ⎛ r (0) r (1) r (2) ... r (M − 1) ⎟ ⎜ r (1) r (0) r (1) ... ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ r (2) r (1) r (0) ... ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎠ ⎝ r (M − 1) ... ... ... r (0) a1 a2 a3 aM ⎞ ⎛ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ = − ⎜ ⎟ ⎜ ⎟ ⎜ ⎠ ⎝ r (1) r (2) r (3) r (M) ⎞ ⎟ ⎠ R a O M 2 y (n) M y (n) = − (aky (n − k)) + u (n) minak E k=1 u (n) {ak} y (n) + M k=1 (aky 2 (n − k)) = minak E y2 (n) + 2 M E [y2 (n)] + 2 M k=1 (akE [y (n) y (n − k)]) + M M k=1 minak y (n) ɛ2 = r (0) + 2 a1 a2 a3 ... aM r (1) r (2) r (3) ... r (M) k=1 (aky (n) y (n − k)) + l=1 (akalE [y (n − k) y (n − l)]) ⎛ ⎜ ⎜ ⎝ ⎛ ⎞ ⎜ ⎜ ⎝ r (0) r (1) r (2) r (1) r (0) r (1) r (2) r (1) r (0) ... ... ... r (M − 1) ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ r (M − 1) ... ... ... r (0) a1 a2 a3 aM ⎞ ⎟ ⎠ + M k=1 (ak
Page 1: Digital Filter Design By: Douglas L
Page 4 and 5: Digital Filter Design By: Douglas L
Page 7: L ∞
Page 10 and 11: H (ω) = M−1 −(iωn) h=0 h (n)
Page 12 and 13: H (ω) = A (ω) e−(iθ0) M−1
Page 14 and 15: ∀n, 0 ≤ n ≤ M − 1 : (h [n])
Page 16 and 17: h [n] h [n] = h [−1] M
Page 18 and 19: ∞ M W (ω)
Page 20 and 21: x = cos (ω) E (ω) = W
Page 22 and 23: L + 2 ⎛ ⎜ ⎝ 1 cos (ω0) c
Page 24 and 25: O 16L 2 O L 3 L
Page 26 and 27: M L∞ E (ω) = W (ω
Page 28 and 29: H (s) = ∞ ha (t) e −∞ −(st
Page 30 and 31: H (s) = LHP H (s) = √ 2
Page 32 and 33: B λ 2 1 = 1 + ɛ2CM 2 (λ) CM 2
Page 34 and 35: L ∞ Ha (s)
Page 36 and 37: L ∞ L ∞ L
Page 38 and 39: ∀n : (h (n) = ha (nT ))
Page 40 and 41: n > 0 M h (n) = − (akh (n
Page 44 and 45: ∂ 2 ɛ ∂a = 2r + 2Ra R
Page 46 and 47: ∂ 2 ɛ ∂a = 2r + 2Ra R
Page 48 and 49: ∂ 2 ɛ ∂a = 2r + 2Ra R

Download This File - The Free Information Society

Create successful ePaper yourself

Delete template?

Save as template?