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
