Chapter 3

Lesson Objectives

Equations

Chapter 3.1.1

Signals and Noise Digital Signals are much less prone to interference and so I theory should produce higher quality signals e.g. Digital TV and Radio

Sampling 1 Instead of storing a whole waveform a signal can be sampled (digitised) at regular intervals. As long as the signal is sampled at a high enough frequency the original signal can be reconstructed

Sampling Problems 1 If you sample at the wrong frequency then the original signal cannot be reconstructed accurately. The optimum sampling frequency is: 2x the highest frequency in the original signal e.g. a music CD need a highest frequency of 20kHz to be stored so music is sampled at 44.1kHz.

Sampling Problems 2 Another problem is that if you sample at too a low frequency then spurious frequencies called aliases can be created in the reconstructed signal

Wheels moving backwards You have probably seen this effect on TV or the cinema when a car moving forwards appears to have wheels that are rotating backwards

Software Demo  Looking Less Often  Activity 70S

Digitising Signals can be digitised by turning the sampled waveform into numbers. Sampling is done using an analogue to digital converter (ADC) A Digital to analogue converter (DAC) can reverse the process The diagram on the left shows that with 3 bits of information up to 8 levels can be stored (3 bits = 8 possible binary numbers) Using more bits means more levels and a greater resolution A telephone uses 8 bits = 256 levels for each sample A high quality CD uses 16 bits = levels for each sample

Chapter – 3.1.3

Signal Transmission A fax converts text and pictures into pixels one line at a time. This is slow and requires a lot of data to be transferred Slow information transfer rate

Signal Transmission sends less information per page because it can encode letters as numbers instead of pixel by pixel. This means a faster information transmission time even if we use the same transmission rate (64000 bits per second) as the fax machine

Chapter 3.2

Sending digital data 1 Channel Capacity needed to send signal Resolution (number of bits) of each sample Sampling rate (must be 2x highest frequency in the signal spectrum)

Sending digital data 2 speech sampled at 8000 Hz 8 bits used per sample bits per second (64 kHz) need to be sent Telephone sampled at 44.1kHz 16 bits used per sample bits per second to be sent (0.7 MHz) 2 Stereo channels doubles this to 1.4 MHz This is in the medium wave radio band CD Quality

Waves all around Look at the size of TV aerials on the roofs of houses - they give you and idea of the wavelengths being received. Usually the rods are half a wavelength long – a few cm

TV Ariel's The rods are a few cm long indicating that it is designed to receive waves with wavelengths of a few cm

Chapter

Polarisation TV and Radio waves are polarised To pick up a signal the receiving rods must be parallel to the electric field oscillations of the wave Again looking at TV aerials will tell you the direction of polarisation

TV Ariel's The short Transverse rods indicate that this ariel is designed to receive waves that are horizontally polarised

Chapter 3.2.3

Making Music If you are a Jazz Maverick and Electro-pop superstar its important that you know how to process sounds and music…

Oboe

Clarinet

Xylophone

Snare Drum

1000Hz Pure Tone

1000Hz and 3000hz combined

White Noise

Software Demo  Cleaning up a sound  Activity 210S

Chapter 3.2.4

Bandwidth The width of the frequency spectrum of a signal Telephone 3100 Hz (300 Hz to 3400Hz) Music 20 to 40 kHz The faster you need to transmit the greater the bandwidth needed Greater Bandwidth means the higher the frequency band needed

Software Demo  Bits per second and bandwidth  Activity 260S

Bandwidth and sampling Roughly speaking you need a bandwidth = to the maximum rate of transmission of bits Maximum digital signalling rate in bits per second = 2 x bandwidth needed B Bandwidth B = 1/T where T is the time one bit is “on”