Lecture One

Question 1

What is a signal?

Answer 1

The representation of how a quantity i.e pressure, voltage etc changes over time

Question 2

Describe the recording of a signal:

Answer 2

1) Capture (Data Acquisition)
2) Filter (Signal Conditioning)
3) Measure (Feature Extraction)
4) Question (Hypothesis testing)

Question 3

What does Data Acquisition break down into?

Answer 3

1) Signal transduction
2) Conditioner
- A/D converter-
3) Sampler
4) Quantizer

Question 4

What is transduction?

Answer 4

Converts one form of energy i.e pressure into another i.e voltage

Voltage used as this is the only format computers can use

Question 5

What is notable about the output of the transducer signal?

Answer 5

The analogue voltage (output) waveform of a transducer should be identical to the original waveform

Question 6

Convert degrees to radians;

Answer 6

90 = Pi/2 radians
180 = Pi radians
270 = 3 Pi / 2 radians
360 = 2 Pi

Question 7

What is trig?

Answer 7

SohCahToa

Opposite = Y
Adjacent = X

X = A cos (2ft . Phase)
Y = A sin (2ft . Phase)

Question 8

What are signals most commonly?

Answer 8

Sinusoidal

Question 9

How can a sinusoid wave be described?

Answer 9

Amplitude (A)
Frequency (Hz)
Phase

Question 10

What is phase?

Answer 10

Amount a sinusoid has been shifted relative to another

in radians

Question 11

Are all periodic signals sinusoidal?

Answer 11

Not all periodic (cyclic) signals are sinusoidal HOWEVER, all periodic signals can be constructed by superpostion (summation) of sinusoids of different frequencies, amplitudes and phases.

Question 12

What sort of signals are not periodic?

Answer 12

Transient signals

Question 13

Describe each stage of the data acquisition in terms of notation?

Answer 13

Conditioner x(t)
Sampler x[n]
Quantizer Xq[n]

Question 14

What conditions do x(t) meet?

Answer 14

original signal/waveform

Continuous in both time (t) and value (amplitude)

Question 15

What conditions do x[n]?

Answer 15

Sampled signal
Discrete-time (fixed number of samples), but continuous value (amplitude)
n(also N) denotes a single sample

Question 16

What conditions do Xq[n]?

Answer 16

Discrete in bothtime and value
Sampled and quantized signal
‘Final’ computer-friendly format

Question 17

Why do sample?

Answer 17

We sample an analogue signal to get it to a form suitable for storage and processing on a computer

Analogue to Digital conversion (A/D converter; ADC)

Question 18

Describe sampling notation?

Answer 18

Sampling interval (sampling period; T) is the time interval between samples (e.g. xseconds)

Sampling frequency (fs) is the number of samples in a second (e.g. xHz)

Question 19

Whats the problem with too many samples?

Answer 19

If too many samples are made (oversampling), then the resulting dataset could be unmanageable (storage and/or processing)

Less of a problem these days (computer storage is getting cheaper)

Question 20

Whats the problem with too few samples?

Answer 20

It should be obvious that too few samples will result in a poor representation of the original signal

Remember that our transducer selection should also ensure that transducer voltage output reflects original signal –so too should the sampled data

Question 21

What is aliasing?

Answer 21

When a sinusoid is sampled at too low a frequency, a sinusoid of lower frequency results

Question 22

What is the equation for aliasing?

Answer 22

Fresult = Fsample- f original

Check slide for further examples

Question 23

What does aliasing result in?

Answer 23

High frequency components will be aliased to low-frequency components and will interact with genuine low-frequency components

Irreversible loss of information (i.e. unable to reconstruct original signal)

Destructive (out of phase) or constructive (in phase)

Question 24

What is the nyquist criterion?

Answer 24

If a signal contains no frequencies higher than W, then the original can be reconstructed when sampled at 2W

Typically sample at greater frequency than 2Wto be safe

Question 25

What is nyquist frequency?

Answer 25

NyquistFrequency is one half the sampling frequency, and is the highest frequency component that can be accurately reconstructed)

Question 26

Does nyquist sampling prevent aliasing?

Answer 26

it will not prevent aliasing occurring

Question 27

What can generate aliasing when sampling rate is good?

Answer 27

High frequency noise (> Nyquistfrequency) present (but unwanted) in the original signal will be aliased to low-frequencies (from 0 Hz to Nyquistfrequency)

Question 28

What can avoid aliasing?

Answer 28

This aliasing can be avoided using a filter to remove (or attenuate) frequency components from the signal prior to sampling

Question 29

What are the two base systems used?

Answer 29

Base ten (10^0-3) i.e 142 = 1x10^2 + 4x10^1 + 2 x10 ^ 0 (1-4 numbers)

Base Two (1-8 Numbers)

2^(0-7)

Question 30

What is quantization?

Answer 30

A quantizertakes a discrete-time (x-axis), continuous-value (y-axis) signal x[n] and produces a quantized value xq[n] that can only take a finite number of values (look at slides if necessary)

Produces an interger from a real number

Question 31

What can happen during quantization?

Answer 31

Clipping can also occur if the signal x[n] is greater or less than the largest or smallest integer value

Question 32

What is the typical AD converter?

Answer 32

Typically 12 or 16 bit A/D converters these days (reduce error)

Question 33

What is the error associated with quantiziation?

Answer 33

There is an error associated with quantization (q[n])

q[n] is the difference between original and quantized signal

Question 34

What is the max error proportional to?

Answer 34

Maximum quantization error (Q) is proportional to the number of bits of A/D conversion

q = max x - min x / 2^n-1