Exponentials and Geometrics

The questions below are due on Thursday March 13, 2025; 02:00:00 PM.
 
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Part a. Find the Continuous-Time Fourier Transform of f_1(t):

f_1(t)=e^{-|t|}

Part b. Find the Continuous-Time Fourier Transform of f_2(t):

f_2(t)=\cases{te^{-t}&if $t>0$\cr0&otherwise\cr}

Part c. Find the Discrete-Time Fourier Transform of f_3[n]:

f_3[n]=\left({1\over2}\right)^{|n|}

Part d. Find the Discrete-Time Fourier Transform of f_4[n]:

f_4[n]=\cases{n\left({1\over2}\right)^n&if $n\ge0$\cr0&otherwise\cr}

Part e. Find the Fourier transform of f_3(t):

f_3(t) = \frac{1}{1+t^2}

Please upload a single pdf file that contains your answers to all parts of this problem:

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