In [2]:

```
from sympy.mpmath import quad
from math import log10
# To compute the mean square error distortion and output signal-to-distortion ratio.
#Given data
l1=1# # 1st Quantization level
l2=3# # 2nd Quantization level
l3=5# # 3rd Quantization level
l4=7# # 4th Quantization level
U1=(l1+l2)/2# # upper boundary of 1st level
U2=(l2+l3)/2# # upper boundary of 2nd level
U3=(l3+l4)/2# # upper boundary of 3rd level
U4=l4+(U1-l1)# # upper boundary of 4th level
L1=l1-(U1-l1)# # Lower boundary of 1st level
D1=quad(lambda x:(x**3-2*x**2+x)/32,[L1,U1]) # Mean square error distortion of 1st level
D2=quad(lambda x:(x**3-6*x**2+9*x)/32,[U1,U2])# # Mean square error distortion of 2nd level
D3=quad(lambda x:(x**3-10*x**2+25*x)/32,[U2,U3])# # Mean square error distortion of 3rd level
D4=quad(lambda x:(x**3-14*x**2+49*x)/32,[U3,U4])# # Mean square error distortion of 4th level
D=D1+D2+D3+D4# # Total square error distortion
P=quad(lambda x:x**3/32,[L1,U4])# # Signal power
SDR=10*log10(P/D)# # Output signal-to-distortion ratio.
# Displaying the result in command window
print '\n The mean square error distortion = %0.3f'%(D)#
print '\n The output signal-to-distortion ratio = %0.2f dB'%(SDR)#
print '\n To minimize the distortion, we need to place the quantization levels closer at amplitudes close to 8 and farther at amplitudes close to zero.'
print '\n This quantizer would be optimal for an input with a uniform pdf.'
```

In [1]:

```
# To compute transmission bit rate, average and peak signal to quantization noise ratio
# Given data
fs=8*10**3# # Sampling frequency in Hz
n=8# # Number of bits per sample
stepsize=10*10**-3# # Time after which step size is recomputed
overhead=5# # Number of overhead bits
N=fs*n# # Number of information bits pe second
Toverhead=overhead/stepsize# # The number of overhead bits/second
# Effective transmission bit rate
bitrate=N+Toverhead# # Transmission bit rate in bps
# Peak signal to quantization noise ratio
PSQNR=6.02*n+4.77# # Peak signal to quantization noise ratio in dB
# Average signal to quantization noise ratio
ASQNR=6.02*n# # Average signal to quantization noise ratio in dB
# Displaying the result in command window
print '\n Effective transmission bit rate = %0.1f kbps'%(bitrate*10**-3)#
print '\n Peak signal to quantization noise ratio = %0.2f dB'%(PSQNR)#
print '\n Average signal to quantization noise ratio = %0.2f dB'%(ASQNR)#
```

In [2]:

```
# To compute the minimum encoding rateof given 4 sub-band coder
# Given data
N=4# # Total number of sub-bands
L1=225# # Lower limit of first sub-band
U1=450# # Lower limit of first sub-band
L2=450# # Lower limit of second sub-band
U2=900# # Lower limit of second sub-band
L3=1000# # Lower limit of third sub-band
U3=1500# # Lower limit of third sub-band
L4=1800# # Lower limit of fourth sub-band
U4=2700# # Lower limit of fourth sub-band
E1=4# # Encoding bit of first sub-band
E2=3# # Encoding bit of second sub-band
E3=2# # Encoding bit of third sub-band
E4=1# # Encoding bit of fourth sub-band
# Sampling rate of the sub-bands according to Nyquist theorem
sr1=2*(U1-L1)# # Sampling rate of first sub-band in samples/second
sr2=2*(U2-L2)# # Sampling rate of second sub-band in samples/second
sr3=2*(U3-L3)# # Sampling rate of third sub-band in samples/second
sr4=2*(U4-L4)# # Sampling rate of fourth sub-band in samples/second
# Total encoding rate
SR=sr1*E1+sr2*E2+sr3*E3+sr4*E4# # Total encoding rate in bps
# Displaying the result in command window
print '\n Total encoding rate = %0.1f kbps'%(SR*10**-3)#
```

In [6]:

```
from __future__ import division
# To find the upper bound of the transmission bit rate
# Given data
FL=810*10**6# # Lower limit of forward channel frequency band
FU=826*10**6# # Upper limit of forward channel frequency band
N=1150# # Number of simultaneous users#
SE=1.68# # Spectral efficiency in bps/Hz
CR=0.5# # Coder rate
bandused=90/100# # 90% bandwidth is used
bandwidth=bandused*(FU-FL)# # Total bandwidth available for traffic channels in Hz
Cbandwidth=bandwidth/N# # Maximum channel bandwidth in Hz
ChannelDR=SE*Cbandwidth# # Maximum channel data rate in bps
DR=ChannelDR*CR# # Maximum net data rate in bps
# Displaying the result in command window
print '\n Maximum net data rate = %0.1f kbps'%(DR*10**-3)#
```

In [7]:

```
from __future__ import division
# To compute the gross channel data rate
# Given data
t=20*10**-3# # Duration of encoding of one block in second
B1=50# # The first bits in Type-1 channel
CRC1=10# # Number of CRC bits in Type-1 channel
FEC=0.5# # FEC rate for Type-1 channel
B2=132# # Next bits in Type-2 channel
CRC2=5# # Number of CRC bits in Type-2 channel
B3=78# # The last bits in Type-3 channel
N1=(B1+CRC1)/FEC# # Total number of bits transmitted in Type-1 channel
N2=(B2+CRC2)# # Total number of bits transmitted in Type-2 channel
N3=B3# # Total number of bits transmitted in Type-3 channel
N=N1+N2+N3# # Total number of channel bits transmitted enery t seconda
# The gross channel data rate
BR=N/t# # The gross channel data rate in bps
# Displaying the result in command window
print '\n The gross channel bit rate = %0.2f kbps'%(BR*10**-3)#
```