Problem Solving-Digital Communication Systems-Lecture Slides, Slides of Digital Communication Systems

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Digital Communication

Systems

Dr. Shurjeel Wyne

Lecture 8

Problem Solving (CH3)

The raised cosine filter

 Raised-Cosine Filter

 Nyquist filter (pulse) having No ISI at sampling time

f W

W W f W W W

f W W

f W W

H f

0 for| |

for 2 | |

cos

1 for| | 2

0

(^20)

0 

Excess bandwidth: W  W 0 Roll-off factor 0

0 W

W W r

  0  r  1

2 0

0 0 0 1 [ 4 ( ) ]

cos[ 2 ( ) ] ( ) 2 (sinc( 2 )) W W t

W W t h t W W t  

 



W = absolute bandwidth , W 0 =1/(2T) is minimum Nyquist Bandwidth

RC

RC

The Raised cosine filter – cont’d

Baseband sSB ( 1 )

R s

W   r

| H ( f )|| HRC ( f ) |

r  0

r  0. 5

r  1 r  1

r  0. 5

r  0

h ( t )  hRC ( t )

2 T

1 4 T

3 T

1 4 T

 3 2 T

 1 T

 1

1

0

1

 3 T ^2 T  T 0 T 2 T 3 T

Passband W DSB ( 1  r ) R s

Roll-off factor 0

0 W

W W r

  0  r  1

Adjust r according to trade-off between Excess bandwidth and sensitivity to timing error

Two Types of Degradation in Error

Performance of Digital Signalling

 Loss in signal-to-noise ratio

 Distortion e.g., due to ISI

Bottoming out of BER versus Eb/N curve (due to ISI distortion) cannot be avoided by increasing Eb/N

NOTE: Read article 3.3. from the textbook for further details