Lecture One Flashcards
What is a signal?
The representation of how a quantity i.e pressure, voltage etc changes over time
Describe the recording of a signal:
1) Capture (Data Acquisition)
2) Filter (Signal Conditioning)
3) Measure (Feature Extraction)
4) Question (Hypothesis testing)
What does Data Acquisition break down into?
1) Signal transduction
2) Conditioner
- A/D converter-
3) Sampler
4) Quantizer
What is transduction?
Converts one form of energy i.e pressure into another i.e voltage
Voltage used as this is the only format computers can use
What is notable about the output of the transducer signal?
The analogue voltage (output) waveform of a transducer should be identical to the original waveform
Convert degrees to radians;
90 = Pi/2 radians 180 = Pi radians 270 = 3 Pi / 2 radians 360 = 2 Pi
What is trig?
SohCahToa
Opposite = Y Adjacent = X
X = A cos (2ft . Phase) Y = A sin (2ft . Phase)
What are signals most commonly?
Sinusoidal
How can a sinusoid wave be described?
Amplitude (A)
Frequency (Hz)
Phase
What is phase?
Amount a sinusoid has been shifted relative to another
in radians
Are all periodic signals sinusoidal?
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.
What sort of signals are not periodic?
Transient signals
Describe each stage of the data acquisition in terms of notation?
Conditioner x(t)
Sampler x[n]
Quantizer Xq[n]
What conditions do x(t) meet?
original signal/waveform
Continuous in both time (t) and value (amplitude)
What conditions do x[n]?
Sampled signal
Discrete-time (fixed number of samples), but continuous value (amplitude)
n(also N) denotes a single sample
What conditions do Xq[n]?
Discrete in bothtime and value
Sampled and quantized signal
‘Final’ computer-friendly format
Why do sample?
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)
Describe sampling notation?
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)
Whats the problem with too many samples?
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)
Whats the problem with too few samples?
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
What is aliasing?
When a sinusoid is sampled at too low a frequency, a sinusoid of lower frequency results
What is the equation for aliasing?
Fresult = Fsample- f original
Check slide for further examples
What does aliasing result in?
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)
What is the nyquist criterion?
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
What is nyquist frequency?
NyquistFrequency is one half the sampling frequency, and is the highest frequency component that can be accurately reconstructed)
Does nyquist sampling prevent aliasing?
it will not prevent aliasing occurring
What can generate aliasing when sampling rate is good?
High frequency noise (> Nyquistfrequency) present (but unwanted) in the original signal will be aliased to low-frequencies (from 0 Hz to Nyquistfrequency)
What can avoid aliasing?
This aliasing can be avoided using a filter to remove (or attenuate) frequency components from the signal prior to sampling
What are the two base systems used?
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)
What is quantization?
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
What can happen during quantization?
Clipping can also occur if the signal x[n] is greater or less than the largest or smallest integer value
What is the typical AD converter?
Typically 12 or 16 bit A/D converters these days (reduce error)
What is the error associated with quantiziation?
There is an error associated with quantization (q[n])
q[n] is the difference between original and quantized signal
What is the max error proportional to?
Maximum quantization error (Q) is proportional to the number of bits of A/D conversion
q = max x - min x / 2^n-1
