Chapter 9: Analog Signals

Example 9.1, Page 235

In [1]:
#Variable Declaration

Bs=4.2  #Signal Bandwidth(MHz)
delf=2.56  #Deviation Ratio

#Calculation

delF=Bs*delf  #Peak Deviation(MHz)
BIF=2*(delF+Bs)  #Signal Bandwidth(MHz)
BIF=round(BIF,1)
#Results

print "The peak deviation is:" , delF,"MHz"
print "Signal Bandwidth is" , BIF,"MHz"

The peak deviation is: 10.752 MHz
Signal Bandwidth is 29.9 MHz

Example 9.2, Page 236

In [2]:
#Variable Declaration

delF=200 #Peak Deviation(kHz)
f=0.8    #Test tone frequency (kHz)

#Calculation

m=delF/f  #Modualtion index
B=2*(delF+f)  #Bandwidth of the signal(kHz)

#Results

print "The modulation index is" , m
print "Bandwidth of the signal is", B,"kHz"

The modulation index is 250.0
Bandwidth of the signal is 401.6 kHz

Example 9.3, Page 236

In [3]:
#Variable Declaration

Bs1=4.2  #Signal Bandwidth(MHz) of Example 9.1
delf=2.56  #Deviation Ratio of Example 9.1

delF2=200 #Peak Deviation(kHz) of Example 9.2
Bs2=0.8    #Test tone frequency (kHz) of Example 9.2

#Calculation

delF1=Bs1*delf  #Peak Deviation(MHz) of Example 9.1

BIF1=2*(delF1+2*Bs1)  #Signal Bandwidth(MHz) of Example 9.1 according to Carson's rule
BIF1=round(BIF1,1)
BIF2=2*(delF2+2*Bs2)  #Signal Bandwidth(kHz) of Example 9.2 according to Carson's rule.

#Results

print "Signal Bandwidth of Example 9.1 by Carson's rule is",BIF1,"MHz"

print "Signal Bandwidth of Example 9.2 by Carson's rule is",BIF2,"kHz"

Signal Bandwidth of Example 9.1 by Carson's rule is 38.3 MHz
Signal Bandwidth of Example 9.2 by Carson's rule is 403.2 kHz

Example 9.4, Page 241

In [4]:
import math
#Variable Declaration

delf=5 #Deviation frequency (kHz)
Bs=1   #Test Tone Frequency (kHz)
CNR=30  #Carrier to noise ration(dB)

#Calculation

m=delf/Bs  #Modulation Index
Gp=3*(m**2)*(m+1)  #Processing gain for sinusoidal modulation
Gp=10*math.log10(Gp) #Converting Gp into dB
SNR=CNR+Gp

Gp=round(Gp,1)
SNR=round(SNR,1)

#Results

print "The receiver processing gain is",Gp,"dB"
print "The Signal to noise ratio is", SNR,"dB"

The receiver processing gain is 26.5 dB
The Signal to noise ratio is 56.5 dB

Example 9.5, Page 245

In [5]:
import math
#Variable Declaration

n=24  #Number of channels
g=13.57  #Peak/rms factor(dB)
b=3.1  #Channel Bandwidth(kHz)
P=4     #Emphasis improvement (dB)
W=2.5   #Noise weighting improvement(dB)
CNR=25  #Carrier to noise ratio (dB)
delFrms=35  #rms value of Peak Deviation(kHz)
fm=108    #Baseband frequency (kHz)
#Calculation
 
L=10**((-1+4*math.log10(n))/20)
g=10**(g/20)  #Converting process gain to ratio
delF=g*delFrms*L  #Peak Deviation(Hz)
BIF=2*(delF+fm)   #Signal Bandwidth(kHz) by Carson's rule
Gp=(BIF/b)*((delFrms/float(fm))**2)  #Processing Gain
Gp=10*math.log10(Gp)  #Converting Gp to dB
SNR=CNR+Gp+P+W  #Signal to noise ratio for top channel in 24-channel FDM basseband signal
SNR=round(SNR,1)
#Results

print "Signal to noise ratio for top channel in 24-channel FDM Baseband signal is", SNR,"dB"

Signal to noise ratio for top channel in 24-channel FDM Baseband signal is 45.7 dB

Example 9.6, Page 246

In [6]:
import math
#Variable Declaration

delF=9  #Peak Deviation (MHz) 
fm=4.2  #Baseband frequency(MHz)
SNR=62  #Signal to noise ration(dB)
M=11.8  #Noise weighing(P)+emphasis improvement(W)-implementation margin(IMP)

#Calculation

D=delF/fm  #Modulation Index
GPV=12*(D**2)*(D+1)  #Processing Gain for TV
GPV=10*math.log10(GPV)  #Converting GPV into dB
CNR=SNR-GPV-M   #carrier to noise ratio(dB)
CNR=round(CNR,1)
#Results

print "The Carrier to noise ratio required at the input of FM detector is",CNR,"dB"

The Carrier to noise ratio required at the input of FM detector is 27.8 dB