1. EE235
Signals and Systems
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2. An ex and a Constant were…
…walking down the street; when a Differentiator walked up to them. Constant started running away, and ex asked him, “what are you doing?!” Constant replied, “If I meet a Differentiator, I will disappear!” ex said, proudly, “I don’t care, I am ex!”, and walked up to the Differentiator. “Hi I am ex,” he said, thumbing his nose… “Hi,” said the Differentiator, “I’m d/dy.”
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3. Today’s menu Posted: Textbook chapters (on website/blog) To do:
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From Friday (Signals x and y relationships)
End of hand-waving
Describing Common Signals
Periodicity
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4. Signals: Digging in Types of signals
Some “standard” signals (alphabets!)
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5. 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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6. Signal types Continuous time / Discrete time
An x-axis relationship
Discrete time = “indexed” time
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7. Signals: Notations
A continuous time signal is specified at all values of time, when time is a real number.
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8. Signals: Notations
A discrete time signal is specified at only discrete values of time (e.g. only on integers)
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9. 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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10. 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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11. 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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12. 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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13. Brake! X-axis: continuous and discrete
Y-axis: continuous (analog) and discrete (digital)
Our class: (mostly) Continuous time, analog values (real and complex)
Clear so far?
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14. Common signals (memorize)
Building blocks to bigger things
constant signal t a
unit step signal t 1
u(t)=0 for t<0
u(t)=1 for t≥0
r(t)=0 for t<0
r(t)=t for t≥0
r(t)=t*u(t) for t≥0
unit ramp signal t 1
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15. Sinusoids/Decaying sinusoids
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16. Decaying and growing
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17. Generalizing the sinusoids
General form: x(t)=Ceat, a=σ+jω
Equivalently: x(t)=Ceσtejωt
Remember Euler’s Formula?
x(t)=Ceσtejωt
amplitude
Sinusoidal with frequency ω (in radians)
Exponential
(3 types)
What is the frequency in Hz?
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18. Remember how to convert between the two?
Imaginary signals
Remember how to convert between the two? z r a b
z=a+jb real/imaginary
z=rejΦ magnitude/phase f
real
imag
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19. Describing signals Of interest? s(t) t Peak value +/- time?
Complex? Magnitude, phase, real, imaginary parts?
Periodic?
Total energy?
Power?
s(t) t
Time averaged
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