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H (ω) = M−1 −(iωn) h=0 h (n) e = h (0) + h (1) e−(iω) + h (2) e−(i2ω) + · · · + M−1 −(iω M−1 M−1 iω −(iω h (M − 1) e −(iω(M−1)) = e 2 ) h (0) e 2 + · · · + h (M − 1) e M−1 −(iω e 2 ) (h (0) + h (M − 1)) cos M−1 2 ω + (h (1) + h (M − 2)) cos M−3 2 ω + · · · + i (h (0) − h (M − 1)) 2 ) e −(iθ0) ω θ0 = 0 h (0) + h (M − 1) = h (0) − h (M − 1) = h (1) + h (M − 2) = h (1) − h (M − 2) = =
h (k) = h ∗ (M − 1 − k) θ0 = 0 θ0 = π 2 e−(iθ0) = −i h (0) + h (M − 1) = h (0) − h (M − 1) = ⇒ h (k) = − (h ∗ (M − 1 − k)) θ0 = 0 h (k) = h (M − 1 − k) θ0 = π 2 h (k) = − (h (M − 1 − k))
Page 1: Digital Filter Design By: Douglas L
Page 4 and 5: Digital Filter Design By: Douglas L
Page 7: L ∞
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 42 and 43: opt = V H V −1 V H h
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

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