UNIT-5 Filter Designing

INTRODUCTION The Digital filters are discrete time systems used mainly for filtering of arrays. The array or sequence are obtained by sampling the input analog signals. Digital Filters performs the frequency related operations such as Low-pass, High-pass, Band Reject,Band Pass and all pass etc. 10/16/2015D.MOHAN Assoc.Professor ECM Dept 2

The Design specifications include cut-off frequency, sampling frequency of I/P signal, Pass band variation, stop band attenuation approximation, type of filter and realization form etc Digital filters can be realized through hardware or software. Actually speaking, the software digital filters need digital hardware for their operations 10/16/2015D.MOHAN Assoc.Professor ECM Dept 3 INTRODUCTION

Analog Low Pass Filters Model 10/16/2015D.MOHAN Assoc.Professor ECM Dept 4

Digital Low Pass Filters Model 10/16/2015D.MOHAN Assoc.Professor ECM Dept 5

Digital LPF Example 10/16/2015D.MOHAN Assoc.Professor ECM Dept 6

Comparison of Analog &Digital Filters 10/16/2015D.MOHAN Assoc.Professor ECM Dept 7

Types of Digital Filters Two types (1). Finite Impulse Response (FIR) (2). Infinite Impulse Response (IIR) 10/16/2015D.MOHAN Assoc.Professor ECM Dept 8

Finite Impulse Response (FIR)  Basically these are Linear Time Invariant(LTI)Systems So these are characterized by unit sample response.  The FIR systems has finite duration unit sample response. i.e. h(n)=0 for n =M  Unit sample response exist only for the duration for 0 to M-1.Hence this is FIR.  Out put of FIR depends only upon present and past inputs since it is non –recursive i.e. it does not use feedback 10/16/2015D.MOHAN Assoc.Professor ECM Dept 9

 These are also Linear Time Invariant(LTI)Systems So these are characterized by unit sample response.  The IIR systems has infinite duration unit sample response. i.e. h(n)=0 for n<0  Unit sample response exist only for the duration from 0 to ∞.Hence this is IIR  Out put of IIR depends only upon present input as well as past inputs and out puts. Since it is recursive i.e. it uses feedback 10/16/2015D.MOHAN Assoc.Professor ECM Dept 10 Infinite Impulse Response (IIR)

Design Techniques 10/16/2015D.MOHAN Assoc.Professor ECM Dept 11

Analog filter Design 10/16/ D.MOHAN Assoc.Professor ECM Dept

Analog Filter Design 10/16/ D.MOHAN Assoc.Professor ECM Dept

Analog Filter Design 10/16/ D.MOHAN Assoc.Professor ECM Dept

Analog Filter Design 10/16/ D.MOHAN Assoc.Professor ECM Dept

Analog Filter Design 10/16/ D.MOHAN Assoc.Professor ECM Dept

Analog Filter Design 10/16/ D.MOHAN Assoc.Professor ECM Dept

Analog Filter Design 10/16/ D.MOHAN Assoc.Professor ECM Dept

Analog Filter Design 10/16/ D.MOHAN Assoc.Professor ECM Dept

Butterworth Low-pass Filter 10/16/ D.MOHAN Assoc.Professor ECM Dept

Chebyshev Low-pass Filters 10/16/ D.MOHAN Assoc.Professor ECM Dept

Elliptic Low-pass Filter 10/16/ D.MOHAN Assoc.Professor ECM Dept

How do we design a Filter? 10/16/ D.MOHAN Assoc.Professor ECM Dept

Analog Filter Design 10/16/ D.MOHAN Assoc.Professor ECM Dept

Design of Butterworth Low-pass Filter 10/16/ D.MOHAN Assoc.Professor ECM Dept

10/16/ D.MOHAN Assoc.Professor ECM Dept Design of Butterworth Low-pass Filter

10/16/ D.MOHAN Assoc.Professor ECM Dept Design of Butterworth Low-pass Filter

10/16/ D.MOHAN Assoc.Professor ECM Dept Design of Butterworth Low-pass Filter

10/16/ D.MOHAN Assoc.Professor ECM Dept Design of Butterworth Low-pass Filter

10/16/ D.MOHAN Assoc.Professor ECM Dept Design of Butterworth Low-pass Filter

10/16/ D.MOHAN Assoc.Professor ECM Dept Design of Butterworth Low-pass Filter

10/16/ D.MOHAN Assoc.Professor ECM Dept Design of Butterworth Low-pass Filter

10/16/ D.MOHAN Assoc.Professor ECM Dept Design of Butterworth Low-pass Filter

10/16/ D.MOHAN Assoc.Professor ECM Dept Design of Butterworth Low-pass Filter

10/16/ D.MOHAN Assoc.Professor ECM Dept Design of Butterworth Low-pass Filter

10/16/ D.MOHAN Assoc.Professor ECM Dept Design of Butterworth Low-pass Filter

10/16/ D.MOHAN Assoc.Professor ECM Dept Design of Butterworth Low-pass Filter

10/16/ D.MOHAN Assoc.Professor ECM Dept Design of Butterworth Low-pass Filter

10/16/ D.MOHAN Assoc.Professor ECM Dept Design of Butterworth Low-pass Filter

10/16/ D.MOHAN Assoc.Professor ECM Dept Design of Butterworth Low-pass Filter

10/16/ D.MOHAN Assoc.Professor ECM Dept Design of Butterworth Low-pass Filter

10/16/ D.MOHAN Assoc.Professor ECM Dept Butterworth Polynomials

Example -1 10/16/2015D.MOHAN Assoc.Professor ECM Dept 43

10/16/2015D.MOHAN Assoc.Professor ECM Dept 44 Solution for Example -1

10/16/2015D.MOHAN Assoc.Professor ECM Dept 45 Solution for Example -1

10/16/2015D.MOHAN Assoc.Professor ECM Dept 46 Solution for Example -1

10/16/2015D.MOHAN Assoc.Professor ECM Dept 47 Solution for Example -1

10/16/2015D.MOHAN Assoc.Professor ECM Dept 48 Solution for Example -1

10/16/2015D.MOHAN Assoc.Professor ECM Dept 49 Solution for Example -1

10/16/2015D.MOHAN Assoc.Professor ECM Dept 50 Example -2

10/16/2015D.MOHAN Assoc.Professor ECM Dept 51 Solution for Example -2

10/16/2015D.MOHAN Assoc.Professor ECM Dept 52 Solution for Example -2

10/16/2015D.MOHAN Assoc.Professor ECM Dept 53 Solution for Example -2

10/16/2015D.MOHAN Assoc.Professor ECM Dept 54 Transformation

Problem : 1 10/16/2015D.MOHAN Assoc.Professor ECM Dept 55

10/16/2015D.MOHAN Assoc.Professor ECM Dept 56 Transformation from LPF to HPF

Problem : 2 10/16/2015D.MOHAN Assoc.Professor ECM Dept 57

Problem : 3 10/16/2015D.MOHAN Assoc.Professor ECM Dept 58

Transformation 10/16/2015D.MOHAN Assoc.Professor ECM Dept 59

Transformation 10/16/2015D.MOHAN Assoc.Professor ECM Dept 60

Transformation 10/16/2015D.MOHAN Assoc.Professor ECM Dept 61

Transformation 10/16/2015D.MOHAN Assoc.Professor ECM Dept 62

Transformation 10/16/2015D.MOHAN Assoc.Professor ECM Dept 63

Summary Analog to Analog Transformation 10/16/2015D.MOHAN Assoc.Professor ECM Dept 64

Example 10/16/2015D.MOHAN Assoc.Professor ECM Dept 65

Solution 10/16/2015D.MOHAN Assoc.Professor ECM Dept 66

Solution 10/16/2015D.MOHAN Assoc.Professor ECM Dept 67

10/16/2015D.MOHAN Assoc.Professor ECM Dept 68 Example