Question

Find the Fourier transform of a one-dimensional rectangle function, and sketch the pair. Show how they can both be delta functions Verify that the FT of a Gaussian is a Gaussian, t2 1 202 2/o2 /2πο2 -x212 s its and so with a2=1, except for the constant 1/V2TT , e own Fourier transform. Show that they can both be delta functions (but not at the same time!). Sketch the transform cases for large and small variance. Note there are several books of cute Fourier transforms! Explain the relationship to the Laplace transform. (Note the use of a contour integral for this.) Sketch these functions, note the zeros, and note the integral: sin(2TTft) 2t,sinc (2ft) 1 ejut,eut, jw 2 -sin(wt)-2t (2TTft) ω -ta

Answer 1

We Rmo Lo that- at2 -o2 4a2 them a givean let et )yt t리 202 let =

Ley fourier trasgern Y(O) 1 XIw) -t2122 1/2ヶ2 L1 V2ヶ2 27 Yt iveo that- 2 ut 212 6 \l thenn 212 YIw) lalnem 28 For san a Narianne

For darrge vauiamce-