Question

Use the Definition to find the Fourier transform of the following functions A.) $f(t) = e^{-bt}u(t - a)$ B.) $f(t) = te^{-at}$ C.) $f(t) = e^{-at}cos(w_ot)$ I believe \"A\" is $\frac{e^{-a(jw+b)}}{(jw+b)}$ \"B\" should be $\frac{1}{(t+jw)^2}$ I need help with the proof

          Use the Definition to find the Fourier transform of the following functions
A.) $f(t) = e^{-bt}u(t - a)$
B.) $f(t) = te^{-at}$
C.) $f(t) = e^{-at}cos(w_ot)$
I believe \"A\" is $\frac{e^{-a(jw+b)}}{(jw+b)}$
\"B\" should be $\frac{1}{(t+jw)^2}$
I need help with the proof

Use the Definition to find the Fourier transform of the following functions
A.) f(t) = e^-btu(t - a)
B.) f(t) = te^-at
C.) f(t) = e^-atcos(wot)
I believe Äïs (e^-a(jw+b))/((jw+b))
B̈s̈hould be (1)/((t+jw)^2)
I need help with the proof

Added by Jordan J.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Stephen Zaffke

Step 1

) The Fourier transform of a function f(t) is given by the integral from -∞ to ∞ of f(t)e^(-jωt) dt. For f(t) = e^(-bt)u(t - a), where u(t - a) is the unit step function (which is 0 for t < a and 1 for t ≥ a), the Fourier transform is given by the integral from a Show more…

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Use the Definition to find the Fourier transform of the following functions: A.) f(t) = e^(-bt)u(t - a) B.) f(t) = te^(-at) C.) f(t) = e^(-at)cos(wt) (jw + b) / (t + jw)^2