1. Signals and SystemsSignals and SystemsSignals and Systems
Tania Stathaki
Location: Room 811b
Extension: 46229
Email: tania@imperial.ac.uk

2. LOGISTICS OF THE COURSE
• Duration
– 20-22 lectures
• Assessment
– 100% exam
– There isn't any coursework or homework

3. LOGISTICS OF THE COURSE
• Notes
– 9 Parts of Theory
– 9 Tutorial Sheets
• Text Book
– A. Oppenheim, A. Wilsky, S. Nawab, Signals
and Systems

4. What is a signal ?
The concept of signal refers to the space
or time variations in the physical state of
an object.

5. Applications
• Electrical Engineering
voltages/currents in a circuit
speech signals
image signals
• Physics
radiation

6. Applications (cont.)
• Mechanical Engineering
vibration studies
• Astronomy
space photos

7. Applications (cont.)
• Biomedicine
EEG, ECG, MRI, X-Rays, Ultrasounds
• Seismology
tectonic plate movement, earthquake prediction
• Economics
stock market data

8. Classification of signals

9. Continuous Time-Discrete Time

10. Continuous Time-Discrete Time

11. 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]

12. 256x256 64x64
2 Dimensions
From Continuous to Discrete: Sampling

13. Analog-Digital

14. Analog signal

15. Digital signal

16. From Analog to Digital: Quantisation

17. Discrete (Sampled) and Digital (Quantized) Image

18. Discrete (Sampled) and Digital (Quantized) Image

19. 256x256 256 levels 256x256 32 levels
Discrete (Sampled) and Digital (Quantized) Image

20. 256x256 256 levels 256x256 2 levels
Discrete (Sampled) and Digital (Quantized) Image

21. Binary ImageBinary Image

22. Digital vs. Analog

23. Digital vs. Analog

24. 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!

25. Periodic-Aperiodic

26. Causal-Anticausal-Noncausal

27. Even-Odd

28. Even-Odd (cont.)

29. Even-Odd (cont.)

30. Even-Odd (cont.)

31. Deterministic-Stochastic

32. Right handed-Left handed

33. Finite length-Infinite Length

34. Electroencephalogram (EEG) Data

35. Stock Market Data

36. Satellite image
Volcano Kamchatka Peninsula, Russia

37. Satellite image
Volcano in Alaska

38. Medical Images:
MRI of normal brain

39. Medical Images:
X-ray knee

40. Medical Images: Ultrasound
Five-month Foetus (lungs, liver and bowel)

41. Astronomical images