ece3101_Homework6_SOLNS_F19.docx - B Olson Convolution/Multiplication Fourier Transform Operations(contin You are also responsible for the examples that

# ece3101_Homework6_SOLNS_F19.docx - B Olson...

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B. Olson Convolution/Multiplication Fourier Transform Operations (contin.) You are also responsible for the examples that we did in class and as class activities 1) Using convolution and/or multiplication operations determine the Fourier transform of the function f(t) Sketch the function and its Fourier Transform. f ( t )= 16 16 + t 2 [ n =−∞ e 4 ( t 2 n ) 2 ] The function, f(t), can be viewed as : f ( t )= 16 16 + t 2 [ n =−∞ δ ( t 2 n )∗ e 4 t 2 ] Visualizing f(t) Resulting f(t)  n n t 2 -6 -4 -2 0 2 4 6 t -2 2 t * t 2 4 t e 2 16 16 t 2 4 2 t n e n t  t 2 16 16 t
Determining F( ) mathematically f ( t )= 16 16 + t 2 [ n =−∞ δ ( t 2 n )∗ e 4 t 2 ] F ( ω ) = 1 2 π { 16 16 + t 2 } ∗ℑ { n =−∞ δ ( t 2 n ) } ⋅ℑ { e 4 t 2 } ( T = 2 ω 0 = 2 π T = π ) = 1 2 π { 16 e 4 | ω | } { ω 0 k =−∞ δ ( ω 0 ) } { π 4 e ω 2 / 16 } = 1 2 π { 16 e 4 | ω | } { π k =−∞ δ ( ω ) } {

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• Fall '18
• James Kang

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