Analogue Sampling

Question 1

What is the benefit of digital transmission?

Answer 1

Even when there is considerable noise added to the signal from transmission we are still able to obtain the original data.
Error detection and correction can be used.
Encryption algorithms can be used.
Multiplexing can be used so that multiples users can be on the same channel.
[IMAGE 14]

Question 2

What is an ADC?

Answer 2

Analogue to digital converter.

Question 3

What is analogue continuous and analogue discrete?

Answer 3

Continuous: has a value at any point across the x/time axis.
Discrete: only shows the value at certain x/time point
[IMAGE 22]

Question 4

What is digital continuous and digital discrete?

Answer 4

Continuous: Has a value at any point across the x/time axis.
Discrete: only shows the value at certain x/time point
[IMAGE 23]

Question 5

What is a casual wave?

Answer 5

This is a wave that starts from t = 0

Question 6

What is a non-casual wave?

Answer 6

this is a wave that is continuouse between -∞ < t < ∞

Question 7

What is the Dirac Delta function?

Answer 7

This is a concept function that is not found naturally in physics.
The function is 0 at all points except when t = 0.
When t = 0 the function is undefined.
The area under the function is 1 between -∞ and ∞ so the height of the spike when t = 0 must be ∞ large
[IMAGE 24]

Question 8

For the common Dirac delta function (See image), explain why this is a Dirac delta function?««»>

Answer 8

Becuase the are under each square is 1 and the function only occurs when t = 0

Question 9

What is a pulse train?

Answer 9

This is lots of Dirac delta functions which periodically occur at points of time.
[IMAGE 26]

Question 10

What is the Dirac delta function for a pulse train?

Answer 10

[IMAGE 27]

Question 11

How does the Dirac Delta function apply to an ADC with an input function f(t)?

Answer 11

If you multiply the two together then at any point ‘a’ you will have a pulse for the input function.
[IMAGE 28]

Question 12

How does sampling work?

Answer 12

You sample an analogue signal at specific periodic points so that it can then be stored in data and can be reconstructed later?

Question 13

How fast do you need to sample an input?

Answer 13

Sampling frequency must be higher than the highest frequency in the sample. (Ts < T , fs > f)
As a general rule:
fs > 2f
Ts < 0.5t

Question 14

What is undersampling?

Answer 14

This is when you don’t sample fast enough soo you do not get a signal that can be reproduced later.
[IMAGE 29]

Question 15

What is the Nyquist - Shannon theorem?

Answer 15

This is the theory that the sampling frequency should be twice the highest frequency contained in the signal
fs > 2f

Question 16

What is quantization?

Answer 16

This is when the voltage of samples taken of a wave are limited to certain defined voltage levels.
The voltage levels stored are the nearest to the actual voltage level

Question 17

What is quantization noise?

Answer 17

Because quantization does not produce the exact voltage level, the errors from quantization produce noise in the signal.
[Image 30]

Question 18

What is the equation to calculate noise power?

Answer 18

Power = ∆^2 / 12
Where 1/∆ is the gradient of the slope for the signal.
Slope = (y2 - y1) / (x2 - x1)
(y2 - y1) = 1 because we are quantising at specific intervals
Slope = 1 / (x2 - x1)