GROUP MEMBERS

ELISHBA KHALID 07-CP-07

TAHIRA SAMEEN 07-CP-31

INFINITE IMPLUSE RESPONSE

PRESENTATION LAYOUT Introduction IIR Systems IIR FiltersTypes of IIR

Filters

Block DiagramUses Of IIRApplications Of

IIRConclusion

INTRODUTION

Sample of output is the weighted sum of past and current samples of input

Property of signal processing systems

IIR SYSTEM

IIR systems have an infinite impulse response

Opposite to FIRConsider Time Zero

FILTERS

Filter the SignalProcess Of Compressing SystemElectronic Systems

FILTER REPRESENTATION Difference equationRecursive computation needs y[-1] and y[-2])

Transfer function

][]2[81]1[

21][ kxkykyky

21

21

81

211

1)()()(

)()(81)(

21)(

zzzXzYzH

zXzYzzYzzY

IIR FILTERS

Property of IIR Types Fast And Cheap Poor Bandpass Filtering

TYPES OF IIR FILTERS

Analog Digital

DIGITAL IIR FILTERS Infinite Impulse Response (IIR) filter has impulse

response of infinite duration, e.g.

implement the IIR filter

][21 kukh

k

1

1

0

211

1 41

21

21 )(

zzzzH k

k

k

...Z

)()( 21)( )(

211

1)()()( )()()( 1

1zXzYzzYzX

zzXzHzY

zXzYzH

][]1[21][ ][]1[

21][ )()(

21)( 1 kxkykykxkykyzXzYzzY

Recursively compute output, given y[-1] and x[k]

Block Diagram

STABILITY Bounded input x[k] such that | x[k] | B <

, then the filter response y[k] is also bounded | y[k] | B <

IIR filter is stable if and only if its poles lie inside the unit circle

|][| khn

STABILITY RULES

For a signal, poles are inside the unit circle

Unit circle is in the region of convergence.

All FIR filters are stable

MATLAB COMMAND

MATLAB's freqz command displays the frequency responses of IIR filters and FIR filters

USES OF IIR FILTERSNoise removal

Example: bandpass filtering to suppress out-of-band noise

Spectral analysis, synthesis, and compressionExamples: calculating power spectra

APPLICATION

• Data conversion • Channel equalization • Carrier frequency and phase

recovery

REFRENCES

http://www.Wikipideia.com http://www.google.com Lectures Of Prof.Brian L.Evains Signals and System By OOPENHEM

CONCLUSION

THANKS