lecture15,16-digitalfilters

8/13/2019 Lecture15,16-DigitalFilters

http://slidepdf.com/reader/full/lecture1516-digitalfilters 1/16

DIGITAL FILTERS: AN INTRODUCTION

ڻڇ دع:رت ه

ل16،17Lecture 16, 17ڻع محا سحا



Introduction to filters

A filter is a system that attenuates some frequency

components of a signal more than it does others.

It is usually used to eliminate/reduce the energy

contained in some frequency band(s) while retainingthe energy contained in other frequency band(s)



Applications

Filters can be applied to the signal to be

transmmitted (to remove the carrier and a side

band)

For anti-aliasing before sampling a signal

For removing noise from a received signal



Filter bands

Pass band

Stop band

Transition band

1+1

1-1

Passbandripple

wp ws

2



Filter types

Low Pass Filter

Passes frequencies smallerthan a cut-off

High Pass Filter

Passes frequencies higherthan a cut-off

Band Pass Filter

Passes frequencies between

two cut-offs Band Elimination Filter

Passes frequencies otherthan those b/w two cut-offs

ڻڇ را ڍن يڍن ک م صخ

تث راوڻڇ را

يڏو ک م صخ را تثڻڇ را ٽپ

يراو ٻ مئ وچ را تث

ڻڇ ڪور ٽپ يراو ٻ مئ ج وچ

ور تث



ڻڇ را ڍن لخIdeal Low Pass Filter

-wc wc

w

|H(w)|

(w)

w

B



ڻڇ را ڏو لخHigh Pass Filter

|H(w)|

wc

w

w

(w)



ڻڇ را ٽپ لخIdeal Band Pass Filter

-w0w0

B

w

w

|H(w)|

(w)



ڻڇ ڪور ٽپ لخIdeal Band Stop Filter

|H(w)|

(w)

w

w



ت ج ڻڇ گياAnalog Filter Approximations

Butterworth

Chebyshev

Type 1

Type 2

ر ٽبذسق1

سق2



ڻڇ دعDigital Filters

Take digital Input

Digitized Speech

Image

Any other signal that is either digital by nature or isdigitized

Give out Digital Output

Might be implemented in Hardware

Software



ت ج ڻڇ دعDigital Filter Approximations

Finite Impulse Response (FIR) Filters

Their impulse response is time-limited

Also called non-recursive filters and all-zero

filters

Infinite Impulse Response (IIR) Filters

Their impulse response is time-unlimited

Also called recursive filters



Comparison b/w FIR and IIR

Do not have any analogcounterpart

Have linear phase response

Simple to implement, do notrequire feedback

Certain responses are notpractical to implement with FIRfilters

Require more computations /memory

Always Stable

Have an analog counterpart

Have non-linear phase response Difficult to implement, require

feedback

One can implement any responses

with IIR filters

Require less computation/ memory

Stability not always gauranteed

FIR IIR



Comparison b/w FIR and IIR

Less susceptible to the effectof using a limited number of

bits to implement filters suchas round off noise, andcoefficients quantization error

Use FIR if the number offilter coefficients is not toolarge and in particular if littleor no phase distortion isdesired.

More susceptible to theeffect of using a limited

number of bits to implementfilters such as round offnoise, and coefficientsquantization error

Use IIR when there arerequirements such as sharpcutoff and high throughput.

FIR IIR



IIR Filters

Requires feedback

Output is fucntion of the present input, the past

inputs and the past outputs

T M n yaT n yaT n ya

T Ln xbT n xbnT xbnT y

M

L

....21

....1

21

10

L

i

M

i

ii T in yaT in xbnT y0 1

(1)



FIR filters

No feedback

Output is function of the present input and the past

inputs

Output does not depend on the previous outputs

Replace ‘a’ coefficients by zeros in equation (1)

L+1 is said to be the filter length

T N n xbT n xbnT xbnT y N ....110

L

i

i T in xbnT y0

lecture15,16-digitalfilters

Documents