Signalling

Here is a simplified overview of the basic ideas of signalling

Signal Technology

An analogue signal is one which changes continuously from femtosecond to femtosecond and can take on absolutely any value it likes, positive or negative, so that if, for example, the signal is a pressure, you can distinguish very clearly between 1.000000000000000000 pPa and 1.000000000000000001 pPa. A digital signal, on the other hand, is one that only has two possible values and which is only allowed to change from one to the other at predetermined times.

Some systems work with only one of these two types of signal. Examples include two people conversing in front of the fire, an AM or FM radio broadcast of a concert, a vinyl record being played (all analogue only), or a Morse code message being sent via oil lamps on a cornish beach (digital only). Other systems rely on a two-way inter-conversion between the systems. Examples include web-cams and CDs.

The full conversion process involves

a transducer to convert the original analogue signal to an analogue voltage,
sampling,
analogue to digital conversion (ADC),
encoding a carrier,
transmission,
decoding the carrier,
digital to analogue conversion (DAC),
smoothing,
a transducer to convert the reconstructed analogue signal to a form convenient for perception.

Only if the stages in purple are present does the process count as 'digital'. The digital signal is a series of on/off pulses (known as 'bits') representing binary numbers.

Note the somewhat curious idea that information is a quantity with a unit. It is measured in bits. So any question that asks 'how much information?' is expecting an answer in bits.

Resolution

This can mean a number of things.

the number of pixels altogether (eg 20 Mpixel as the resolution of a digital camera)
the number of pixels in a specified length (eg 300 dpi as the resolution of a printer)
the numbers of pixels in two semi-specified lengths (eg a screen resolution of 1028 x 760 pixels)
the size of a pixel
the distance apart two items in an object need to be in order to be represented by different bits of information
the number of levels used in sampling an analogue waveform (eg 24-bit resolution (about 16 million levels) for CDs)
the angle subtended at the device by the smallest distance apart that two objects can be and yet still be 'resolved' into separate images - this can be diffraction-limited by the size of the aperture on the device or pixel-limited by the image-capturing system.

You need to let the context guide you. You can use a formula

Resolution = original size / smallest recordable chunk (or the other way up)

in some circumstances, if you like.

Bandwidth

Suppose you are sending a digital signal on a carrier of 100 MHz with a bandwidth of 1 MHz, so that you have a frequencies of 99-101 MHz to play with. Clearly you will only be able to modulate your carrier at 1 MHz, so this is the maximum rate of sending binary bits. So the data transmission rate depends partly on the bandwidth you have been allocated.

Signal construction

Amplitude-modulated carrier wave

Application: Radio

The high frequency carrier wave is amplified by a factor proportional to the signal.
The resultant wave may be regarded as composed of fourier components whose frequencies are f_carrier, f_carrier±f_signal, etc.
The range of frequencies in the frequency spectrum is known as the bandwidth: no other transmission may have its carrier frequency in this region.

Digitised wave

Application: CDs, multiplexed telephone.

The voltage produced by the microphone is sampled every now and again. If this is not done very often, high-frequency Fourier components will be lost and the fidelity will suffer. A rough guide is to sample at just over twice the highest frequency you wish to capture (the Nordquist Theorem), so that you pick up crests and troughs, thereby defining a wave.
The magnitude of the sampled voltage is turned into binary by an Analogue to Digital Converter (ADC). In a binary representation, high voltages code for 1s and zero for 0s.
If the signal gets degraded, it may be reconstructed be recognising that any old rubbish above a certain voltage level is almost certainly a 1 (or string of 1s). The system is therefore immune from noise.
The string of 1s and 0s (bits) representing a particular level can usually be transmitted in a far shorter time than the chosen time between samples. This makes multiplexing possible.

Pulsed carrier wave

Application: Radar, ultrasound, sonar

The carrier frequency might be very high for radar (0.3 GHz to 30 GHz), high for ultrasound (1.5 MHz to 20 MHz) or quite high for sonar (40 kHz to 400 kHz). All are well above the audible range.

The modulator only allows a signal through when the clock output is high.

Signal transmission

Radio

Suitable for radio (medium wave, VHF), TV (UHF, microwave), satellites for telecomms , GPS, weather, etc (microwave).

Note that for beaming up to a satellite you need a wide dish to avoid diffraction (the width of the beam is approximately l/b, where b is the slit/dish width).

When transmitting from the satellite, you need a narrow-ish dish, with b chosen so that the beam just spreads enough to engulf the earth.

When receiving from a satellite you need a big dish to gather as much energy as possible, accepting that you will have to be accurate in pointing at the satellite (diffraction again).

Optical fibre

The composite signal (see Digitised Wave in Signal Construction above) is applied to an LED (with a series resistor to prevent the LED being overloaded)
The pulses of light are totally internally reflected in the fibre because the angle between the ray and the normal is considerably bigger than the critical angle.
The light is confined to the fibre as it bends round corners.
The emergent light affects the LDR and causes a reconstruction of the original signal to appear at V_out. (see the first section of the 'Sensors' page).

Copper (twisted wire pairs, co-axial)