PROBLEM SET 3: DIGITAL TRANSMISSION AND RAISED COSINE
FILTER
QUESTION 1:
Consıder the raised cosine roll-off filter given by transfer function:
1,



  (| f |  f1 )  
 1
He ( f )  
1  cos 
,
2
2
f








 0,

0 | f | f1
f1 | f | B
| f | B
And impulse response
he (t )  2 f 0 (
sin 2 f 0t  cos 2 f  t 
)
2 
2 f 0t
1  (4 f  t ) 
where fΔ is defined as fΔ = B – f0 . and f1 = f0 -fΔ. f0 is defined as the 6 dB badwidth of the filter.
The roll of factor r = fΔ/ f0.
a) Plot He(f) for r = 0.75, indicating f1 and f0 as well as B on your sketch.
b) Plot He(f) for r = 0.75 in terms of 1/f0.
NOTE: Use Matlab to plot.
QUESTION 2:
Find the PSD (power sprectral density) of the waveform out of an r=0.5 raised cosine roll-off channel
(filter) when the input is a polar NRZ signal. Assume that equally likely binary signalling is used and
the channel bandwidth is large enough to prevent ISI.
Note: Che channel does not distort the signal in terms of intersymbol interference.
QUESTION 3:
Multilevel data with an equivalent bit rate 2400 bit/s is sent over a channel using four level line code
that has a rectangular pulse shape at the output of the Tx. The overall transmission system (i.e
transmitter, channel and receiver) has an r = 0.5 raised cosine Nyquist filter characteristic.
a) Find the baud rate of the received signal
b) Find the 6-dB badwidth for this transmission system.
c) Find the absolute bandwidth for this system.
Note: Research is required for the 6-dB bandwidth and the absolute bandwidth. Make sure also that
you understand the difference between baud rate and bit rate.