2: Signalling_checked

Question 1

Why are digitised signals possible?

Answer 1

Analogue signals [information] can be coded into binary digits which can then be transmitted in multiple ways e.g. along an optical fibre or copper cable.

Question 2

What are digital signals represented by?

Answer 2

Digital signal are represented by Binary numbers (digits)

Question 3

What are the advantages of digital over analogue signals?

Answer 3

1. Digital signals can often be sent, received and reproduced more easily than analogue signals because they can only take a limited number of values.
2. Digital files can be compressed to reduce their size, and manipulated easily for artistic effect
3. Digital signals are more resistant to the effects of Noise
4. Computers can be used to easily process digital signals, since computers are digital devices too

Question 4

What are the disadvantages of digital over analogue signals

Answer 4

1. Digital signals can never reproduce analogue signals exactly - some information will always be lost
2. Because digital signals can be copied more easily, digital information (films, music etc.) can be reproduced illegally unlimited number of times.
3. Confidential information, such as personal data and photos, may be stolen and copied without the owner’s knowledge or consent, more easily by hackers, infected networks or malicious websites.

Question 5

Are Analogue signals limited in the values they can take?

Answer 5

No. Analogue signals also vary continuously from one value to the next.

Question 6

1. How can a weak signal be strengthened?
2. What is noise in the context of signals?
3. When you transmit an electronic signal, it will pick up noise. From what does it pick up noise?
4. What is a problem with amplifying a signal with noise

Answer 6

1. A weak signal can be amplified.
2. Noise appears as random variation on the signal
3. Noise is picked up from Electrical disturbances or other signals
4. The disadvantage is that noise is amplified as well

Question 7

Why is it easier to reconstruct the original signal from the noisy signal with digital signals?

Why is it important that it’s easy to reconstruct the signal

Answer 7

This is much easier with digital than analogue signals because the number of values a digital signal can take is limited

You need to get an accurate representation of what was sent

Question 8

Can Analogue signals be digitised?

What is the process called, define it

Answer 8

Yes. Analogue signal can be digitised

The process is digitising, its the process in which the value of a continuous analog signal is taken at regular time intervals and converted into the nearest digital values.

Question 9

How do you digitise a signal, where each sample taken is coded with 3 bits?

Identify a potential problem/limitation?

Answer 9

A sample with 3 bits means that there are N=2³ levels called quantisation levels [or alternative levels] to represent the signals value.

You take the value of the signal at regular time intervals then find the nearest quantisation level.

Each quantisation level is represented by a binary number so you can convert the analogue values to binary numbers

Limitation :The digital signal you end up with won’t be exactly the same as the analogue signal if the nearest quantisation level doesn’t match the signal when a sample is taken

Question 10

What 2 factors affect how well a digitised signal matches the original?

Answer 10

1. The number of samples per second - this must be at least twice the highest frequency in the signal to ensure that all the frequencies within the signal are transmitted [and reconstructed] correctly
2. The number of bits per sample - this must be high enough that the transmitted signal closely matches the original but not so high that it is negatively affected by noise.

Question 11

What happens if a signal is digitised using only a few, widely spaced samples?

Answer 11

A low sapling rate can create low frequency signals - called aliases - that were not in the original signal at all

Question 12

What is quantisation error?

Answer 12

The quantisation error for a sample is the difference between the value of the input signal and the quantised signal. Quantisation errors can be reduced by increasing the number of levels; however, as the number of levels increases, so does the number of bits needed to represent each sample.

Question 13

What is the advantage of increasing quantisation levels?

Answer 13

The more closely the digitised signal will match the original

Question 14

What is resolution?

State an equation for resolution.

A signal is detected over a 12V range, 8 bit sample of this signal is produced, calculate resolution of this sample

Answer 14

Resolution is determined by the number of bits in the binary number representing the digital values - the greater the number of bits the greater the resolution.

Resolution = potential difference range / number of quantisation levels

12V range / 2⁸(256)

= 0.047V

Question 15

What is the advantage of using a lower resolution?

Answer 15

Using a lower resolution reduces the demand on data storage and transmission speeds

Question 16

What limits the number of bits that can be used for sampling, and so limits the number of quantisation levels [alternative levels]?

Answer 16

Noise. If the original signal contains noise then you would sampling the noise to greater detail rather than ignoring it.

You should not have a smaller gap between quantisation levels [alternative levels] than the size in noise variation

Question 17

How do you calculate maximum number of useful quantisation levels?

Answer 17

max useful levels = total pd of noisy signal variation / pd of noise variation

= V_total / V_noise

Question 18

How do you determine the number of bits required for maximum useful quantisation levels?

Q: a signal has a max total variation of 200mV. the noise variation is 5mV. calcualte the largest number of bits per sample worth using to encode the variation

Answer 18

b = log₂ [V_total / V_noise ]

log₂ 0.2V / 0.005V = 5.3, so this goes up to 6 bits

We go up to 6 bits because 5 bits gives an insufficient 32 levels,

The V_total / V_noise gives 40 max and this will be covered by 6 bits.

Question 19

List 2 conditions that must be met for accurately reconstructing a signal

Answer 19

1. The number of samples per second - this must be at least twice the highest frequency in the signal to ensure that all the frequencies within the signal are reconstructed accurately.
2. The number of bits per sample - this must be high enough that the transmitted signal closely matches the original but not so high that it is negatively affected by noise.

Question 20

State the Nyquist Theorem:

Minimum sampling rate =

Answer 20

Minimum sampling rate = Twice the highest frequency component

Nyquist Theorem

Question 21

Why does the sampling rate have to be high?

Answer 21

To record all the high frequency detail of the signal

To avoid the creation of aliases

Question 22

What are aliases?

Answer 22

Low frequency signals that are created from having a too low sampling rate. These low frequency signals are not part o the original signal.

Question 23

What is the sampling rate for music?

How do you ensure aliasing doesn’t occur?

Answer 23

The human ear can’t detect frequencies above 20KHz, so for music to be sampled accurately, it is sampled at a frequency of 44.1KHz.

Filters remove frequencies above 20kHz in the original signal so aliasing doesn’t occur

Question 24

What can be the result of not sampling frequently enough and not filtering out frequencies above a maximum

Answer 24

By not sampling frequently enough, you lose high frequency details.

If frequencies above a maximum value are not filtered out as well, then the low sampling rate can also create false low frequencies which is known as aliasing from frequencies above the max limit

Question 25

Define bit rate.

Answer 25

The bit rate tells us how many bits of data are processed every second. Bit rates are usually measured in kilobits per second (kbps)

Question 26

1. State an equation for bit rate and give a unit.
2. A cd uses 16 bits per sample at a sample rate of 44.1kHz for 2 channels. calculate combined bit rate for 2 channels

Answer 26

Bit rate = samples per second

= (sample rate (Hz or KHz)) * bits per sample

(16 * 44100) * 2 = 1.4 * 10⁶ bits s^-1

= 1.4MHz

Question 27

How can you speed up the process of uploading images?

Answer 27

Compress your image to reduces the file size

This also uses less storage

Question 28

How do you calculate duration of signal?

A song occupies 28Mbytes of memory on a phone. if the bit rate is 1.4MHz for the system, calculate the duration of signal

Answer 28

Time taken = number of bits in signal / bit rate

= (28 * 10⁶) * 8 / 1.4 * 10⁶

= 160s

= 2 mins 40 sec

Question 29

How do you calculate the number of bits required for storing a recording that lasts 3.5 minutes with a sample rate of 40KHz where there are 16 bits per sample

Answer 29

bits = number of seconds * sample rate (samples per second) * bits per each sample

seconds = 210 Seconds,

there are 40000 samples per second each with 16 bits

210 * 40000 * 16 = 134400000

= 134.4 Mbits

Question 30

What does it mean if an image has a 6 bit resolution

Answer 30

bit resolution means the image uses 6 bits per pixel

Question 31

What is meant by speed of transmission

Answer 31

Speed at which the signal travels