# Chapter 7 : Mathematical Representation of Noise¶

## Example 7.3 Page No : 413¶

In :
import math

#The resismath.tance R  =  1000 Ohm
R  =  10**3;

#The Capacitance C  =  0.5*10**-6 F
C  =  0.1*10**-6;

#Cutoff frequency for RC filter is f
f  =  1./(2*math.pi*R*C)

#White noise power spectral density n
n  =  10**(-9);

#Noise power at filter output P
P  =  (math.pi/2)*n*f;

print 'Noise power at output filter is ',P,' Watt'

#Noise power at filter output P_new when cutoff frequency is doubled
P_new  =  (math.pi/2)*n*2*f;

print 'Noise power at output filter when cutoff frequency is doubled is ',P_new,' Watt'

#Ideal Low Pass filter Bandwidth B  =  1000 Hz
B  =  1000.;

print 'Output Noise Power is ',n*B,' Watt'

print 'Output Noise Power when cut-off frequency is doubled is ',2*n*B,' Watt'

#Proportionality consmath.tant T  =  0.01
T  =  0.01;

#Output noise power O
O  =  n*(B**3)*(T**2)*(4./3)*(math.pi)**2;

print 'Output Noise Power when signal is passed through a differentiator passed through ideal low pass filter %.4f'%O,' Watt'

O_new  =  8*n*(B**3)*(T**2)*(4./3)*(math.pi)**2;

print 'Output Noise Power when signal is passed through a differentiator passed through ideal low pass\
\n filter and when cut-off frequency is doubled is %.4f'%O_new,' Watt'

Noise power at output filter is  2.5e-06  Watt
Noise power at output filter when cutoff frequency is doubled is  5e-06  Watt
Output Noise Power is  1e-06  Watt
Output Noise Power when cut-off frequency is doubled is  2e-06  Watt
Output Noise Power when signal is passed through a differentiator passed through ideal low pass filter 0.0013  Watt
Output Noise Power when signal is passed through a differentiator passed through ideal low pass
filter and when cut-off frequency is doubled is 0.0105  Watt


## Example 7.4 Page No : 413¶

In :
import math

#Given signal strength S  =  0.001 W
S  =  0.001;

#Gaussian Noise Magnitude n
n  =  10**(-8);

#Frequency of signal f  =  4000 Hz
F  =  4000.;

#Noise at equalizer output N

def f8(f):
return n*(1+(f**2)/F**2)


SNR value is  9.7197  dB