ELEC2134 > Signals

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• (d^2 x)_dt+3 dx_dt+2x=4e^(−3t) u(t)
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• Applications of Laplace Transforms
• Applications
• Aside_ Convolution
• Aside_ Linear Time Invariant (LTI) systems
• Complex Fourier Series
• Convolution Operator ∗
• Convolution
• Example - Dirac Delta
• Example - Exponential decay (when a_0)
• Example - Unit step function
• Example
• Exercises
• F(s)=1_((s+1) (s+2)^2 )=A_(s+1)+B_(s+2)+C_(s+2)^2
• Fourier Series
• Fourier Transform
• Frequency Spectrum
• Given v_c (0)=0, i_c (0)=0
• Initial Conditions
• Laplace Transform
• Other Transform Pairs
• Partial Fraction Expansions
• Poles and Zeroes
• Power in a Fourier Series
• Properties of the Fourier Transform
• Properties
• SUMMARY
• The Big Picture - Fourier Transforms
• The Dirac Delta
• The Signum Function
• The Unit Step Function
• Y(s)=(s−2)_(s(s+1)^3 )=A_s+B_(s+1)+C_(s+1)^2 +D_(s+1)^3
• deg⁡(numerator)≥deg⁡(denominator)
• f(t)=(2−3e^(−10t)+e^30t )u(t)
• f(t)=tu(t)
• s(s^2+2s+5)