Digital Filter Structure Short notes | Digital Signal Processing - Electronics and Communication Engineering (ECE) PDF Download

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Short Notes on Digital Filter Structure
1. In tro duction
• Digital filters pro cess discrete-time signals to mo dify or extract c haracteristics (e.g., noise remo v al,
frequency selection).
• Filter structure defines ho w the transfer function H(z) is implemen ted using adders, m ultipliers,
and dela ys.
• Key structures: Direct F orm, Canonical F orm, Cascade, P arallel.
2. T ransfer F unction
• General form: H(z) =
?
M
k=0
b
k
z
-k
1+
?
N
k=1
a
k
z
-k
, where b
k
are fee dforw ard and a
k
are feedbac k co e?icien ts.
• Difference equation: y[n] =
?
M
k=0
b
k
x[n -k] -
?
N
k=1
a
k
y[n -k] .
3. T yp es of Digital Filters
• FIR (Finite Impulse Resp onse) : No feedbac k (a
k
= 0 ), inheren tly stable, linear phase p ossible.
• I IR (Infinite Impulse Resp onse) : Includes feedbac k, e?icien t but stabilit y m ust b e ens ured.
4. Common Filter Structures
• Direct F orm I : Separate feedforw ard and feedbac k sections, requires M +N dela ys.
• Direct F orm I I : Com bines sections, uses max(M,N) dela ys, s ensitiv e to quan tization in I IR.
• Canonical F orm : Optimized Direct F orm I I with transp osed signal flo w, memory-e?icien t.
• Cascade F orm : H(z) = H
1
(z) ·H
2
(z) ·... , uses lo w-order sections (e.g., second-order), reduces
quan tization effects.
• P arallel F orm : H(z) =C +H
1
(z)+H
2
(z)+... , suitable for parallel pro cessing, less sensitiv e to
noise.
5. Practical Considerations
• Quan tization Errors : Finite w ord length affects I IR filters; Cascade/P arallel forms are less
sensitiv e.
• Stabilit y : I IR filters require p oles inside unit circle ( |z|< 1 ).
• Computational E?iciency : Direct F orm I I and Canonical minimize memory; Cascade reduces
op erations.
• Round-off Noise : Mitigated b y higher precision or P arallel F orm.
6. Applications
• A udio pro cessing (equalization, noise reduction).
• Comm unications (c hannel filtering).
• Biomedical signal pro cessing (ECG, EEG filtering).
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Page 2


Short Notes on Digital Filter Structure
1. In tro duction
• Digital filters pro cess discrete-time signals to mo dify or extract c haracteristics (e.g., noise remo v al,
frequency selection).
• Filter structure defines ho w the transfer function H(z) is implemen ted using adders, m ultipliers,
and dela ys.
• Key structures: Direct F orm, Canonical F orm, Cascade, P arallel.
2. T ransfer F unction
• General form: H(z) =
?
M
k=0
b
k
z
-k
1+
?
N
k=1
a
k
z
-k
, where b
k
are fee dforw ard and a
k
are feedbac k co e?icien ts.
• Difference equation: y[n] =
?
M
k=0
b
k
x[n -k] -
?
N
k=1
a
k
y[n -k] .
3. T yp es of Digital Filters
• FIR (Finite Impulse Resp onse) : No feedbac k (a
k
= 0 ), inheren tly stable, linear phase p ossible.
• I IR (Infinite Impulse Resp onse) : Includes feedbac k, e?icien t but stabilit y m ust b e ens ured.
4. Common Filter Structures
• Direct F orm I : Separate feedforw ard and feedbac k sections, requires M +N dela ys.
• Direct F orm I I : Com bines sections, uses max(M,N) dela ys, s ensitiv e to quan tization in I IR.
• Canonical F orm : Optimized Direct F orm I I with transp osed signal flo w, memory-e?icien t.
• Cascade F orm : H(z) = H
1
(z) ·H
2
(z) ·... , uses lo w-order sections (e.g., second-order), reduces
quan tization effects.
• P arallel F orm : H(z) =C +H
1
(z)+H
2
(z)+... , suitable for parallel pro cessing, less sensitiv e to
noise.
5. Practical Considerations
• Quan tization Errors : Finite w ord length affects I IR filters; Cascade/P arallel forms are less
sensitiv e.
• Stabilit y : I IR filters require p oles inside unit circle ( |z|< 1 ).
• Computational E?iciency : Direct F orm I I and Canonical minimize memory; Cascade reduces
op erations.
• Round-off Noise : Mitigated b y higher precision or P arallel F orm.
6. Applications
• A udio pro cessing (equalization, noise reduction).
• Comm unications (c hannel filtering).
• Biomedical signal pro cessing (ECG, EEG filtering).
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• Con trol systems (resp onse shaping).
7. Conclusion
• Digital filter structures enable e?icien t implemen tation of signal pro cessing tasks.
• Choice of structure dep ends on stabilit y , computational resources, and application requiremen ts.
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