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Signals and SystemsSignals and SystemsSignals and Systems
Tania Stathaki
Location: Room 811bExtension: 46229Email: [email protected]
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LOGISTICS OF THE COURSE
• Duration
– 20-22 lectures
• Assessment
– 100% exam
– There isn't any coursework or homework
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LOGISTICS OF THE COURSE
• Notes
– 9 Parts of Theory
– 9 Tutorial Sheets
• Text Book
– A. Oppenheim, A. Wilsky, S. Nawab, Signals
and Systems
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What is a signal ?
The concept of signal refers to the space
or time variations in the physical state of
an object.
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Applications
• Electrical Engineering
voltages/currents in a circuit
speech signals
image signals
• Physics
radiation
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Applications (cont.)
• Mechanical Engineering
vibration studies
• Astronomy
space photos
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Applications (cont.)
• BiomedicineEEG, ECG, MRI, X-Rays, Ultrasounds
• Seismologytectonic plate movement, earthquake prediction
• Economics
stock market data
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Classification of signals
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Continuous Time-Discrete Time
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Continuous Time-Discrete Time
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From Continuous to Discrete: Sampling
0 10 20 30 40 50 60-10
-5
0
5
10
Observed signal x(t)
continuous time
0 10 20 30 40 50 60-10
-5
0
5
10
discrete time
Observed signal x[n]
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256x256 64x64
2 Dimensions
From Continuous to Discrete: Sampling
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Analog-Digital
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Analog signal
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Digital signal
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From Analog to Digital: Quantisation
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Discrete (Sampled) and Digital (Quantized) Image
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Discrete (Sampled) and Digital (Quantized) Image
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256x256 256 levels 256x256 32 levels
Discrete (Sampled) and Digital (Quantized) Image
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256x256 256 levels 256x256 2 levels
Discrete (Sampled) and Digital (Quantized) Image
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Binary ImageBinary Image
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Digital vs. Analog
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Digital vs. Analog
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Analog-Digital
Examples of analog technology
• photocopiers
• telephones
• audio tapes
• televisions (intensity and color info per scan line)
• VCRs (same as TV)
Examples of digital technology
• Digital computers!
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Periodic-Aperiodic
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Causal-Anticausal-Noncausal
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Even-Odd
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Even-Odd (cont.)
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Even-Odd (cont.)
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Even-Odd (cont.)
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Deterministic-Stochastic
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Right handed-Left handed
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Finite length-Infinite Length
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Electroencephalogram (EEG) Data
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Stock Market Data
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Satellite image
Volcano Kamchatka Peninsula, Russia
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Satellite image
Volcano in Alaska
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Medical Images:
MRI of normal brain
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Medical Images:
X-ray knee
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Medical Images: Ultrasound
Five-month Foetus (lungs, liver and bowel)
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Astronomical images