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Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

Document Description: Digital Filter Structure for Electronics and Communication Engineering (ECE) 2022 is part of Signals and Systems preparation. The notes and questions for Digital Filter Structure have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about Digital Filter Structure covers topics like and Digital Filter Structure Example, for Electronics and Communication Engineering (ECE) 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Digital Filter Structure.

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Digital Filter Structure

The difference equation

Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

If bk= 0 non recursive or all zero filter.

Direct Form – I

Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

1. Easily implemented using computer program.

2. Does not make most efficient use of memory = M+Np+NF delay elements.

Direct form-II

Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

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)

Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

Ex:

Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

Ex:

Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

Parallel Combination of Second Order Section (PSOS)

Ex:

Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

Ex:

Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE) obtain PSOS

Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

A = 8/3 B = 10 C = -35/3

Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

Jury – Stability Criterion

Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

ROWSCOEFFICIENTS

1

2

bb1 …….    bN

bN bN-1 …….  bo

3

4

Co C1 …….    CN-1

CN-1 CN-2 ……. Co

5

6

do d…….    dN-2

dN-2 dN-3 ……. do

.

.

.

2 N-3

r0 r1 r2

Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

i. D(1) > 0

ii. (-1)N D(-1) > 0

Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

Ex:

Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)

1

2

4     3      2     1   1

1     1      2     3   4

3

4

15   11    6     1  

1      6     11   15  

5224    159   79

D(1) = 4+3+2+1+1 = 11 > 0,            (-1)4 D(-1) = 3 >0

Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE) Stable.

Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE)Digital Filter Structure Notes | Study Signals and Systems - Electronics and Communication Engineering (ECE) Ans: Unstable

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