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H (ω) = A (ω) e−(iθ0) M−1 −(iω e 2 ) A (ω) A (ω) M−1 −(iω H (ω) = A (ω) e 2 ) A (ω) A (ω) A (ω) 1 −(iπ |H (ω) | = ±A (ω) = A (ω) e 2 (1−signA(ω))) ⎧ ⎨ 1 x > 0 signx = ⎩ −1 x < 0 − ` ´ M−1 2 ω ∠ω
A (ω) ω ∠ω 2π π A (ω) M−1 2
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 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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