Staffordshire University
Faculty of Computing, Engineering and Technology
Signal Processing
Page 1
SIGNALS, NOISE AND SIGNAL-TO-NOISE
Introduction
Signal
Noise
Signal-To-Noise
August 2005
Staffordshire University
Faculty of Computing, Engineering and Technology
August 2005
Signal Processing
Page 2
SIGNALS, NOISE AND SIGNAL-TO-NOISE
Introduction
A signal (in our case a radio or electronic signal) is something which contains information.
The purpose of the communication system is to transfer the information. The quality of the
received information is affected by noise.
Noise is a term that includes:

Naturally occurring noise and interference, eg background ‘sky’ noise from the universe,
atmospheric noise, lightening etc.

Circuit noise due to the movement of electrons in semiconductors and resistors etc.

Man made noise and interference, eg car ignition, triac control circuits, crosstalk between
circuits, mains ‘hum’ etc.
EMC regulations and proper design and control attempts to minimize ‘man-made’ noise and
interference.
Noise affects the quality of the received signal. For example noise in digital data will cause
the
1’s and 0’s to misread and errors occur. The probability of errors depends on the signal-tomove ratio.
Analogue signals, such as speech or music are affected by noise in the form of ‘hiss’ or
crackle which affects the quality of the signal.
Signal
The two main parameters of a signal relevant to this section are its power S, and its spectral
bandwidth.
The average power (or normalized average power) of a signal is denoted by S.
The signal comprises a band of frequencies and amplitudes, varying from instant to instant in
a random way.
The signal spectrum is usually bandlimited, i.e. it is limited to a bandwidth say BHz, as
illustrated below.
Staffordshire University
Faculty of Computing, Engineering and Technology
August 2005
Signal Processing
Page 3
Signal
f
Signal Power S
Bandlimited Signal
f
B
Noise
Noise is often assumed to be Additive, White, Gaussian noise (AWGN).
Additive - means we assume we can add noise powers and signal powers.
N1
N2
S + N1 + N2
S
White - refers to the spectral density and assumes that the noise appears equally is all parts
of the spectrum (the term is from ‘white’ light which is composed of all colours in the
spectrum). White noise assumes a uniform noise power spectral density of p0 watts per Hz.
Noise
Power
Spectral
Density
p0 watts per Hz
Uniform for all practical frequencies
f
Gaussian – is saying that it is random, with a particular (Gaussian) probability distribution.
Staffordshire University
Faculty of Computing, Engineering and Technology
August 2005
Signal Processing
Page 4
The average or normalized average power of noise is denoted by N.
It is found that the power in a noisy signal is proportional to the bandwidth in which it is
measured as implied by the relationship.
N = p0Bn
Bn is the noise bandwidth in Hz.
p0 is the noise power spectral density in watts per Hz.
p0 is related to the assumption of white noise as shown in the diagram above.
This means that if we allow more bandwidth in the communication system, we will get more
noise.
For example, suppose the noise power spectral density p0, is 1W per Hz. The noise power
for various bandwidths are shown below.
p0
1W
1W
1W
Bn
10Hz
1kHz
10kHz
N
10W
1000W = 1mW
10mW
In communications systems therefore – there is a balance to be found in terms of the
bandwidth allocated :
1)
That it is wide enough to pass the signal with power S and spectral bandwidth B Hz.
2)
That is kept narrow (i.e. no wider that that required for the signal) to limit the noise.
One of the purposes of a filter in a system is to bandlimit noise as illustrated below.
Staffordshire University
Faculty of Computing, Engineering and Technology
Signal Processing
Signal and
Noise Input
August 2005
Page 5
Signal
Poor Signal-to Noise
Noise
f
Band Pass
Filter
B
Signal and
Noise
Output
Signal
f
Improved Signal-to-Noise
Noise
f
In terms of waveforms, this is equivalent to:
Signal and Noise
Input
Signal and Noise
Output
Staffordshire University
Faculty of Computing, Engineering and Technology
August 2005
Signal Processing
Page 6
Signal-To-Noise
The parameter, which gives an indication of the quality of the output, is the signal-to-noise
S .
N
 
Expressed as a ratio this is simply:
Power
S N   Signal
Noise Power
Expressed in decibels, this is:
S N dB  10 log S N 
This may be further developed as:
S N dB  10 log
10
10
S  10 log 10 N
If S and N are in mW, then:
SdBm = 10 log10 S(mW) and NdBm = 10log10 N(mW) and
S N dB = SdBm - NdBm
Some typical values of signal-to-noise are given below:
Good television picture
High Quality Audio
Broadcast Music
Cellular Mobile Radio ET ACS
45dB
80dB
60dB
17dB minimum