Digital Filter Structure
The difference equation
If bk= 0 non recursive or all zero filter.
Direct Form – I
1. Easily implemented using computer program.
2. Does not make most efficient use of memory = M+Np+NF delay elements.
Direct form-II
Smaller no. of delay elements = Max of (M, Np) + NF
Disadvantages of D-I & D-II
1. They lack hardware flexibility, in that, filters of different orders, having different no. of multipliers and delay elements.
2. Sensitivity of co-efficient to quantization effects that occur when using finite -precision
arithmetic.
Cascade Combination of second-order section (CSOS)
Ex:
Ex:
Parallel Combination of Second Order Section (PSOS)
Ex:
Ex:
obtain PSOS
A = 8/3 B = 10 C = -35/3
Jury – Stability Criterion
ROWS | COEFFICIENTS |
1 2 | bo b1 ……. bN bN bN-1 ……. bo |
3 4 | Co C1 ……. CN-1 CN-1 CN-2 ……. Co |
5 6 | do d1 ……. dN-2 dN-2 dN-3 ……. do |
. . . 2 N-3 | r0 r1 r2 |
i. D(1) > 0
ii. (-1)N D(-1) > 0
Ex:
1 2 | 4 3 2 1 1 1 1 2 3 4 |
3 4 | 15 11 6 1 1 6 11 15 |
5 | 224 159 79 |
D(1) = 4+3+2+1+1 = 11 > 0, (-1)4 D(-1) = 3 >0
Stable.
Ans: Unstable
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1. What is a digital filter? |
2. What are the advantages of using a digital filter over an analog filter? |
3. What are the different types of digital filter structures? |
4. How do I choose the appropriate digital filter structure for my application? |
5. Can digital filters be used for real-time signal processing? |
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