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.

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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

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INTRODUCTION

Analog Low Pass Filters Model

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Digital Low Pass Filters Model

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Digital LPF Example

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Comparison of Analog &Digital Filters

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Types of Digital Filters

Two types

(1). Finite Impulse Response (FIR)

(2). Infinite Impulse Response (IIR)

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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<0 and 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

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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

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Infinite Impulse Response (IIR)

Design Techniques

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Analog filter Design

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Analog Filter Design

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Analog Filter Design

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Analog Filter Design

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Analog Filter Design

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Analog Filter Design

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Analog Filter Design

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Analog Filter Design

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Butterworth Low-pass Filter

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Chebyshev Low-pass Filters

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Elliptic Low-pass Filter

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How do we design a Filter?

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Analog Filter Design

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Design of Butterworth Low-pass Filter

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Design of Butterworth Low-pass Filter

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Design of Butterworth Low-pass Filter

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Design of Butterworth Low-pass Filter

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Design of Butterworth Low-pass Filter

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Design of Butterworth Low-pass Filter

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Design of Butterworth Low-pass Filter

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Design of Butterworth Low-pass Filter

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Design of Butterworth Low-pass Filter

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Design of Butterworth Low-pass Filter

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Design of Butterworth Low-pass Filter

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Design of Butterworth Low-pass Filter

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Design of Butterworth Low-pass Filter

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Design of Butterworth Low-pass Filter

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Design of Butterworth Low-pass Filter

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Design of Butterworth Low-pass Filter

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Design of Butterworth Low-pass Filter

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Butterworth Polynomials

Example -1

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Solution for Example -1

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Solution for Example -1

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Solution for Example -1

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Solution for Example -1

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Solution for Example -1

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Solution for Example -1

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Example -2

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Solution for Example -2

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Solution for Example -2

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Solution for Example -2

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Transformation

Problem : 1

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Transformation from LPF to HPF

Problem : 2

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Problem : 3

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Transformation

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Transformation

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Transformation

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Transformation

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Transformation

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Summary Analog to Analog Transformation

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Example

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Solution

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Solution

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Example