1. Signals and Systems
EE235
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2. Climbing every mountain
What do you call a teapot of boiling water on top of K2?
A high-pot-in-use
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3. Extra Fourier Transform
Returning ¾-term
Examples
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4. Fourier Transform: Fourier Transform Inverse Fourier Transform: 4
Weak Dirichlet: Otherwise you can’t solve for the coefficients! 4
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5. Low Pass Filter What is h(t)? (Impulse response) 5
Consider an ideal low-pass filter with frequency response
H(w) w
Looks like an octopus centered
around time t = 0 
Not causal…can’t build a circuit. 5
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6. Low Pass Filter What is y(t) if input is:
Ideal filter, so everything above is gone:
y(t)
Consider an ideal low-pass filter with frequency response
H(w) w 6
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7. Output determination Example
Solve for y(t)
Convert input and impulse function to Fourier domain:
Invert Fourier using known transform: 7
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8. Output determination Example
Solve for y(t)
Recall that:
Partial fraction:
Invert: 8
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9. Describing Signals (just a summary)
Ck and X(w) tell us the CE’s (or cosines) that are needed to build a time signal x(t)
CE with frequency w (or kw0) has magnitude |Ck| or |X(w)| and phase shift <Ck and <X(w)
FS and FT difference is in whether an uncountably infinite number of CEs are needed to build the signal. -B B w t
x(t)
X(w) 9
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10. Describing Signals (just a summary)
H(w) = frequency response
Magnitude |H(w)| tells us how to scale cos amplitude
Phase <H(w) tells us the phase shift
H(w)
cos(20t)
Acos(20t+f)
p/2
magnitude phase A
-p/2 f 20 20
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11. Convolution/Multiplication Summary
The Pair: 11
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