# SIGNALS, NOISE AND SIGNAL-TO-NOISE

Document Sample

```					Staffordshire University
Faculty of Computing, Engineering and Technology         August 2005

Signal Processing                                             Page 1

SIGNALS, NOISE AND SIGNAL-TO-NOISE

Introduction

Signal

Noise

Signal-To-Noise
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-to-
move 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              Bn              N
1W             10Hz            10W
1W             1kHz            1000W = 1mW
1W             10kHz           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                    August 2005

Signal Processing                                                        Page 5

Signal and
Noise Input                   Signal                    Poor Signal-to Noise

Noise
f

Band Pass
Filter
B                                      f

Signal and
Noise
Output                        Signal                    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:          S N   Signal Power
Noise
Power

Expressed in decibels, this is:               S N dB  10 log S N 
10

This may be further developed as:             S N dB  10 log   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                       45dB
High Quality Audio                            80dB