The Fourier transform of a function f (x) is defined as: f (w) = L dx f (ω) -. f (x)e-iwx Similarly, the inverse Fourier transform of a function f (w) whose Fourier transform is known is found as: 1 f(x) = L f (w) e-iwx dw So, find the Fourier transform f (w) for a> 0 of the function given below, and using this result, calculate the inverse Fourier transform to verify the form f (x) given to you: for x > 0 for x <0 e-ax, f (x) = }{
The Fourier transform of a function f (x) is defined as: f (w) = L dx f (ω) -. f (x)e-iwx Similarly, the inverse Fourier transform of a function f (w) whose Fourier transform is known is found as: 1 f(x) = L f (w) e-iwx dw So, find the Fourier transform f (w) for a> 0 of the function given below, and using this result, calculate the inverse Fourier transform to verify the form f (x) given to you: for x > 0 for x <0 e-ax, f (x) = }{
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Transcribed Image Text:The Fourier transform of a function f (x) is defined as:
f (w) = L dx
f (ω) -.
f (x)e-iwx
Similarly, the inverse Fourier transform of a function
f (w) whose Fourier transform is known is found as:
1
f(x) = L f (w) e-iwx dw
So, find the Fourier transform f (w) for a> 0 of the
function given below, and using this result, calculate the
inverse Fourier transform to verify the form f (x) given to
you:
for x > 0
for x <0
e-ax,
f (x) = }{
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