Chapter 6 Baseband Shaping For Data Transmission¶
Example 6.1(a) page 235¶
In [2]:
from __future__ import division
%matplotlib inline
from matplotlib.pyplot import plot,grid,title,show
#Figure 6.1(c):Discrete PAM Signals Generation
# [3].BiPolar NRZ
#page 235
x = [0, 1, 1, 0, 0, 1 ,0 ,0 ,1 ,1]
binary_negative = [-1, -1 ,-1 ,-1 ,-1 ,-1 ,-1 ,-1 ,-1, -1]
binary_zero = [0 ,0 ,0 ,0 ,0, 0 ,0 ,0 ,0 ,0]
binary_positive = [1, 1 ,1 ,1 ,1 ,1 ,1 ,1 ,1 ,1]
L = len(x)
L1 = len(binary_negative)
total_duration = L*L1
#plotting
for i in range(0,L):
if(x[i]==0):
plot(range(i*L-L,i*L),binary_zero)
elif((x[i]==1) and (x[i-1]!=1)):
plot(range(i*L-L,i*L),binary_positive)
else:
plot(range(i*L-L,i*L),binary_negative)
grid()
title('BiPolar NRZ')
show()
Example6.2 Page 241¶
In [1]:
from __future__ import division
b = [0,0,1,0,1,1,0]##input binary sequence:precoder input
a = [1^b[0]]
if(a[0]==1):
a_volts=[1]
for k in range(1,len(b)):
a.append(a[(k-1)]^b[(k)])
if(a[(k)]==1):
a_volts.append(1)
else:
a_volts.append(-1)
print 'Precoder output in binary form:'
for aa in a:
print aa,'\t',
print '\n'
print 'Precoder output in volts:'
for bb in a_volts:
print bb,'\t',
print '\n'
#Duobinary coder output in volts
c= [1+ a_volts[0]]
for k in range(1,len(a)):
c.append(a_volts[(k-1)]+a_volts[(k)])
print 'Duobinary coder output in volts:'
for cc in c:
print cc,'\t',
print '\n'
#Duobinary decoder output by applying decision rule
b_r=[]
for k in range(0,len(c)):
if(abs(c[(k)])>1):
b_r.append(0)
else:
b_r.append(1)
print 'Recovered original sequence at detector oupupt:'
for brr in b_r:
print brr,'\t',
Example6.3 page 246¶
In [2]:
from __future__ import division
#for generating bipolar format
#Refer Table 6.4
x = [0,1,1,0,1,0,0,0,1,1]##input binary sequence:precoder input
y= [1]
for k in range(1,len(x)+1):
y.append(x[(k-1)]^y[(k-1)])
y_delay = y[0:-1]
print 'Modulo-2 adder output:'
for yy in y:
print yy,'\t',
print ''
print 'Delay element output:'
for yyy in y_delay:
print yyy,'\t',
print ''
z=[]
for k in range(0,len(y_delay)):
z.append(y_delay[k])
print 'differential encoder bipolar output in volts:'
for zz in z:
print zz,'\t',
Example 6.4 Page 247¶
In [3]:
from __future__ import division
from numpy import arange,sinc,sin,pi
%matplotlib inline
from matplotlib.pyplot import plot,grid,title,show,xlabel,ylabel
#Different Line Coding Techniques
#[1].NRZ Polar Format [2].NRZ Bipolar format
#[3].NRZ Unipolar format [4]. Manchester format
#[1]. NRZ Polar format
a = 1 # The Amplitude value
fb = 1 # The bit rate
Tb = 1/fb# #bit duration
f = arange(0,1/(100*Tb)+2/Tb,1/(100*Tb))
Sxxf_NRZ_P=[]
Sxxf_NRZ_BP=[]
Sxxf_NRZ_UP=[]
Sxxf_Manch=[]
for i in range(0,len(f)):
Sxxf_NRZ_P.append((a**2)*Tb*(sinc(f[i]*Tb)**2))
Sxxf_NRZ_BP.append((a**2)*Tb*((sinc(f[i]*Tb))**2)*((sin(pi*f[i]*Tb))**2))
if (i==0):
Sxxf_NRZ_UP.append((a**2)*(Tb/4)*((sinc(f[i]*Tb))**2)+(a**2)/4)
else:
Sxxf_NRZ_UP.append((a**2)*(Tb/4)*((sinc(f[i]*Tb))**2))
Sxxf_Manch.append((a**2)*Tb*(sinc(f[i]*Tb/2)**2)*(sin(pi*f[i]*Tb/2)**2))
#Plotting
plot(f,Sxxf_NRZ_P)
plot(f,Sxxf_NRZ_BP)
plot(f,Sxxf_NRZ_UP)
plot(f,Sxxf_Manch)
xlabel('f*Tb------->')
ylabel('Sxx(f)------->')
title('Power Spectral Densities of Different Line Codinig Techniques')
grid()
show()
#Result
#Enter the Amplitude value:1
#Enter the bit rate:1
Example 6.6 page 249¶
In [1]:
from __future__ import division
from numpy import arange,sinc,sin,pi
%matplotlib inline
from matplotlib.pyplot import plot,grid,title,show,xlabel,ylabel
#Figure 6.6(b): Ideal Solution for Intersymbol Interference
rb = 1 # The bit rate
Bo = rb/2#
t =arange(-3,1/100+3,1/100)
x = sinc(2*Bo*t)
plot(t,x)
xlabel('t------>')#
ylabel('p(t)------->')#
title('SINC Pulse for zero ISI')
grid()
show()
Example 6.7 page 250¶
In [3]:
from __future__ import division
from numpy import arange,sinc,sin,pi,zeros,cos
%matplotlib inline
from matplotlib.pyplot import plot,grid,title,show,xlabel,ylabel,legend
#Figure6.7(b):Practical Solution for Intersymbol Interference
#Raised Cosine Spectrum
rb = 1 # The bit rate
Tb =1/rb#
t =arange(-3,1/100+3,1/100)
Bo = rb/2#
Alpha =0# #Intialized to zero
x =t/Tb#
p=zeros([3,len(t)])
for j in range(0,3):
for i in range(0,len(t)):
if((j==2) and ((t[i]==0.5) or (t[i]==-0.5))):
p[j,i] = sinc(2*Bo*t[i])
else:
num = sinc(2*Bo*t[i])*cos(2*pi*Alpha*Bo*t[i])
den = 1-16*(Alpha**2)*(Bo**2)*(t[i]**2)+0.01
p[j,i]= num/den
Alpha = Alpha+0.5#
plot(t,p[0,:])
plot(t,p[1,:])
plot(t,p[2,:])
xlabel('t/Tb------>')
ylabel('p(t)------->')
title('RAISED COSINE SPECTRUM - Practical Solution for ISI')
legend(['ROlloff Factor =0','ROlloff Factor =0.5','ROlloff Factor =1'])
grid()
show()
#Result
#Enter the bit rate:1
Example 6.9 Page 254¶
In [3]:
from __future__ import division
from numpy import arange,sinc,sin,pi,cos
%matplotlib inline
from matplotlib.pyplot import plot,subplot,grid,title,show,xlabel,ylabel
#Caption:Frequency response of duobinary conversion filter
#Figure6.9:Frequency Response of Duobinary Conversion filter
#(a)Amplitude Response
#(b)Phase Response
rb = 8 # the bit rate
Tb =1/rb# #Bit duration
f = arange(-rb/2,1/100+rb/2,1/100)
Amplitude_Response = [abs(2*cos(pi*ff*Tb)) for ff in f]
Phase_Response = [-(pi*ff*Tb) for ff in f]
subplot(3,1,1)
plot(f,Amplitude_Response)
xlabel('Frequency f---->')
ylabel('|H(f)| ----->')
title('Amplitude Repsonse of Duobinary Singaling')
subplot(3,1,3)
plot(f,Phase_Response)
xlabel(' Frequency f---->')
ylabel(' <H(f) ----->')
title('Phase Repsonse of Duobinary Singaling')
show()
Example 6.15 page 259¶
In [1]:
from __future__ import division
%matplotlib inline
from matplotlib.pyplot import plot,grid,title,xlabel,ylabel,show,legend,subplot
from numpy import arange,cos,pi,sinc,sin
#Caption:Frequency response of modified duobinary conversion filter
#Figure 6.15: Frequency Response of Modified duobinary conversion filter
#(a)Amplitude Response
#(b)Phase Response
rb = 8# the bit rate
Tb =1/rb# #Bit duration
f = arange(-rb/2,1/100+rb/2,1/100)
Amplitude_Response = [abs(2*sin(2*pi*ff*Tb)) for ff in f]
Phase_Response = [-(2*pi*ff*Tb) for ff in f]
subplot(3,1,1)
plot(f,Amplitude_Response)
xlabel('Frequency f---->')
ylabel('|H(f)| ----->')
title('Amplitude Repsonse of Modified Duobinary Singaling')
grid()
subplot(3,1,3)
plot(f,Phase_Response)
xlabel(' Frequency f---->')
ylabel(' <H(f) ----->')
title('Phase Repsonse of Modified Duobinary Singaling')
grid()
show()
