1. Signals and Systems
EE235
Leo Lam
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2. Today’s menu Lab – detailed arrangements Homework – vacation week
From yesterday (Intro: Signals)
Intro: Systems
More: Describing Common Signals
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3. Office hours Mine: Monday 10-11am Chris: Wednesday 10-11am
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4. Taking a signal apart A+a0 a0 A sound signal t (seconds) T
Offset (atmospheric pressure)
A sound signal
Frequency
Amplitude
A+a0 a0
t (seconds) T
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5. Frequency = 196 t (seconds) f (Hz) time-domain frequency-domain
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6. t to f
196
293.66
440
659.26
t (seconds)
F (Hz)
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7. Combining signals
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8. Summary: Signals Signals carry information
Signals represented by functions over time or space
Signals can be represented in both time and frequency domains
Signals can be summed in both time and frequency domains
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9. Systems A system describes a relationship between input and output
Examples?
v(t)
g(t)
y(t)
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10. Definition: System
A system modifies signals or extracts information. It can be considered a transformation that operates on a signal.
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11. Motivation: Complex systems
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12. Filters
All kinds, and everywhere
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13. Surprising high pass
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14. Summary: System System transforms an input to an output
System can extract information
System can “shape” signals (filters)
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15. Signals: Digging in Types of signals
Some “standard” signals (alphabets!)
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16. Signals: A signal is a mathematical function x(t)
x is the value (real, complex)  y-axis
t is the independent variable (1D, 2D etc.)  x-axis
Both can be Continuous or Discrete
Examples of x…
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17. Signal types Continuous time / Discrete time
An x-axis relationship
Discrete time = “indexed” time
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18. Signals: Notations
A continuous time signal is specified all values of time, when time is a real number.
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19. Signals: Notations
A discrete time signal is specified at only discrete values of time (e.g. only on integers)
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20. What types are these? 90.3 FM radio transmitted signal
Daily count of orcas in Puget Sound
Muscle contraction of your heart over time
A capacitor’s charge over time
A picture taken by a digital camera
Local news broadcast to your old TV
Video on YouTube
Your voice
(continuous)
(discrete)
(c)
((c))
(d)
(c)
(d)
(c)
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21. Analog / Digital values (y-axis)
An analog signal has amplitude that can take any value in a continuous interval (all Real numbers)
Where Z is a finite set of values
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22. Analog / Digital values (y-axis)
An digital signal has amplitude that can only take on only a discrete set of values (any arbitrary set).
Where Z and G are finite sets of values
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23. Nature vs. Artificial Natural signals mostly analog
Computers/gadgets usually digital (today)
Signal can be continuous in time but discrete in value (a continuous time, digital signal)
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