Applied physics III

Basic Concept: digital and analogue systems

by Benson Mbuya

Digital Systems vs Analogue Systems• A signal is any kind of physical quantity

that conveys information.—Audible speech is certainly a kind of signal, as

it conveys the thoughts (information) of one person to another through the physical medium of sound.

• signal will be used primarily in reference to an electrical quantity of voltage or current that is used to represent or signify some other physical quantity.

• An analogue signal is a continuous signal that contains time-varying quantities. Unlike a digital signal, which has a discrete value at each sampling point, an analogue signal has constant fluctuations.

• Any information may be conveyed by an analog signal; often such a signal is a measured response to changes in physical phenomena, such as sound, light, temperature, position, or pressure. The physical variable is converted to an analogue signal by a transducer.

• A digital signal is a physical signal that is a representation of a sequence of discrete values.

• Digital signals are signals that are represented by binary numbers, "1" or "0". The 1 and 0 values can correspond to different discrete voltage values

Analog vs digital

• Analogy systems are less tolerant to noise, make good use of bandwidth, and are easy to manipulate mathematically.

• However, analogy signals require hardware receivers and transmitters that are designed to perfectly fit the particular transmission.

• If you are working on a new system, and you decide to change your analogue signal, you need to completely change your transmitters and receivers.

Analog vs digital

• Digital signals are more tolerant to noise, but digital signals can be completely corrupted in the presence of excess noise.

• In digital signals, noise could cause a 1 to be interpreted as a 0 and vice versa, which makes the received data different than the original data.

• there are systems in place to prevent this sort of scenario, such as checksums and CRCs, which tell the receiver when a bit has been corrupted and ask the transmitter to resend the data.

•

Analog vs digital

• The primary benefit of digital signals is that they can be handled by simple, standardized receivers and transmitters, and the signal can be then dealt with in software (which is comparatively cheap to change).

• The difference between Digital and discrete—Digital quantity may be either 0 or 1, but

discrete may be any numerical value i.e. 0,1....9.

examples

• The analog clock has no physical limit to how finely it can display the time, as its "hands" move in a smooth, pauseless fashion. The digital clock, on the other hand, cannot convey any unit of time smaller than what its display will allow for. The type of clock with a "second-hand" that jerks in 1-second intervals is a digital device with a minimum resolution of one second.

Analogue example

Analogue example: original phone system

example

• The first telephone was very analog, and in fact the wired phone in your house still works this way

Analog and Noise

All electronic circuits suffer from 'noise' which is unwanted signal mixed in with the desired signal

Analogue and digital systems

• Analogue systems process analogue signals which can take any value within a range, for example the output from an LDR (light sensor) or a microphone.

• An audio amplifier is an example of an analogue system. The amplifier produces an output voltage which can be any value within the range of its power supply.

• Digital systems contain devices such as logic gates, flip-flops, shift registers and counters. A computer is an example of a digital system.

Sampling and Reconstruction

• The process of converting from analog data to digital data is called "sampling".

• The process of recreating an analogue signal from a digital one is called "reconstruction“

• Digitisation of a signal is the process by which an analogue signal is converted to a digital signal.

sampling• The sampling rate when digitising an

analogue signal is defined as the number of samples per. second, and is measured in Hertz (Hz), as it is a frequency. You can calculate the sampling rate using the formula:

• The higher the sampling rate, the closer the reconstructed signal is to the original signal, but, unfortunately, we are limited by the bandwidth available.

• Theoretically, a sampling rate of twice the highest frequency of the original signal will result in a perfect reconstructed signal

Review questions

3. Most sounds created by human speech except for 'ss' and 'ff' have a maximum frequency of 4 kHz. What is a suitable sampling rate for a low-quality telephone?

4. Using a sampling rate of 20 kHz and 3 bits, sample the following signal, and then produce a reconstructed signal. What is the maximum frequency that can be perfectly reconstructed using this sampling rate?

Worked solutions

Qn3 soln:

Qn2 soln:

Qn1 soln:

Qn4 soln

references• http://

www.allaboutcircuits.com/vol_1/chpt_9/1.html• http://

www.stanford.edu/class/cs101/analog-digital.html• http://

www.diffen.com/difference/Analog_vs_Digital• http://en.wikipedia.org/wiki/Analog_signal• http://en.wikibooks.org/wiki/A-level_Physics_(Adv

ancing_Physics)/Digitisation/Worked_Solutions

• http://en.wikibooks.org/wiki/Communication_Systems/Analog_vs._Digital

• http://www.kpsec.freeuk.com/analogue.htm• http://www.wisegeek.com/what-is-an-analog-

signal.htm