Digital Signal ProcessingDigital Signal Processing Lecture · PDF file ·...

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Digital Signal Processing Digital Signal Processing Lecture Sh b h Dr. Shoab Khan

Transcript of Digital Signal ProcessingDigital Signal Processing Lecture · PDF file ·...

Digital Signal ProcessingDigital Signal ProcessingLecture

Sh b hDr. Shoab Khan

All-pass Systems

System with unit magnitude response Basic building Block:

Pole in a zero in 1/a*Pole in a , zero in 1/aReal co-efficient all-pass:

Basic LP system

ωαω jj eeH −)(

Constant group delay α

(

Impulse response symmetric about 2α if 2α integerNo symmetry if Ζ∉α2

Ideal low-pass with Delay

Ideal lowpass with Linear Phase

Ideal Lowpass with Linear Phase

Impulse Response

Pole and Zero Locations

Pole-Zero Plot

Frequency Response

Amplitude and Angle Plot

Linear Phase System

Example: LP Filter

Generalized Linear Phase

Generalized linear phase allows a constant phase shift beside a constant delay.

Generalized Linear Phase

Causal Generalized Linear Phase

Example: Type l Filter

Example: Type II Filter

Example: Type II Filter (cont..)

Example: Type III Filter

Example: Type III Filter

Zeroes for FIR Linear Phase Systems: Type I and II

Zeroes for FIR Linear Phase Systems: Type I and II(cont.)

Zeroes for FIR Linear Phase Systems: Type III and IV

Zero Locations for FIR Linear Phase

Phase Compensation

Summary Analysis Part

Discrete-time representation of signalsLTI tLTI systemDTFT AnalysisZ-transform AnalysisDiscrete-time SamplingDiscrete time Sampling Fourier Transform Analysis of systems with rational system functionwith rational system functionLinear Phase System

Rational system function

Inverse System

1)()( =zHzH i

∏ −M

zd 1 )1(

][][*][ nnhnh i δ=

∏−

=

−⋅== N

k

kk

i

zc

zd

ab

zHzH

1

1

0

0

)1(

)1(

)(1)(

=k 1

Inverse system, stable if all poles and zeros, inside the unit circleminim m phase s stemminimum-phase system

)1()90(50)()90()(5.01)((e q) 11− −

nununhzH nn )1()9.0(5.0)()9.0()( ,9.01

)( (e.q) 1 −−=−

= − nununhz

zH

)1()50(90)()50()(9.01)( 11− −

hzH nn )1()5.0(9.0)()5.0()( ,5.01

)( 11 −−=

−= − nununh

zzH nn

ii