The Heaviside step function, or the unit step function, may be defined as H(t) = 1,...

 

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The Heaviside step function, or the unit step function, may be defined as H(t) = 1, t0, 0, t <0. Basic facts about H(t) are that it is an antiderivative of the Dirac delta function: H'(t) = 5(t), and that its Fourier transform is given by 1 1 == H(w) F[H(t)] + 2 (w).. Find Fourier transform of the following functions: (a) (b) (c) F(e at H(t)); F(eat H(-t)); F(te at H(t)). (d) Find the inverse Fourier transform of the function (hint: use partial franctions and results from a), b) and c)) 12+ Tiw-w F(w)= (w2-2iw-1)(-w + iw-6) The Heaviside step function, or the unit step function, may be defined as H(t) = 1, t0, 0, t <0. Basic facts about H(t) are that it is an antiderivative of the Dirac delta function: H'(t) = 5(t), and that its Fourier transform is given by 1 1 == H(w) F[H(t)] + 2 (w).. Find Fourier transform of the following functions: (a) (b) (c) F(e at H(t)); F(eat H(-t)); F(te at H(t)). (d) Find the inverse Fourier transform of the function (hint: use partial franctions and results from a), b) and c)) 12+ Tiw-w F(w)= (w2-2iw-1)(-w + iw-6)