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H (s) = ∞ ha (t) e −∞ −(st) dt H (iλ) H (s) = b0 + b1s + b2s 2 + ... + bM s M 1 + a1s + a2s 2 + ... + aM s M L ∞ (|H (λ) |) 2 = B λ 2 H (iλ) H (iλ) = b0+b1iλ+b2(iλ)2 +b3(iλ) 3 +... 1+a1iλ+a2(iλ) 2 H (iλ) +... = b0−b2λ2 +b4λ 4 +...+iλ(b1−b3λ 2 +b5λ 4 +...) 1−a2λ2 +a4λ4 +...+iλ(a1−a3λ2 +a5λ4 b0−b2λ +...) 2 +b4λ4 +...+iλ(b1−b3λ2 +b5λ4 +...) 1−a2λ2 +a4λ4 +...+iλ(a1−a3λ2 +a5λ4 +...) = (b0−b2λ2 +b4λ 4 +...) 2 +λ 2 (b1−b3λ 2 +b5λ 4 +...) 2 (1−a2λ2 +a4λ4 +...) 2 +λ2 (a1−a3λ2 +a5λ4 +...) 2 = B λ2 s = iλ B − s 2 p1 p1 p1 −p1 − (p1)
s = iλ B λ2 = B − s2 = H (s) H (−s) = H (iλ) H (− (iλ)) = H (iλ) H (iλ) B − s2 H (s) H (−s) H (s) H (−s) (|H (s) |) 2 = H (s) H (−s) s = iλ H (s) B λ2 B λ2 B λ2 = (|H (λ) |) 2 1 = 1+F (λ2 ) F λ2 α = 1+i √ 2 B − s 2 = B λ 2 2 + λ2 = 1 + λ4 2 − s2 = 1 + s4 √ 2 − s √ 2 + s (s + α) (s − α) (s + α) (s − α) 1 + s N N
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 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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