(a) Show that if f(x) has a Fourier transform, so does f(x - α), and F{f(x -...
Question:
(b) Using (a), obtain formula 1 in Table III, from formula 2.
(c) Show that if fÌ(w) is the Fourier transform of f(x), then fÌ(w - α) is the Fourier transform of eiαxf(x).
(d) Using (c), obtain formula 7 in Table III from 1 and formula 8 from 2.
Transcribed Image Text:
f(w) = F(f) f(x) (1 if -b < x 0) + a' 2 if 0
f(w) = F(f) f(x) (1 if -b < x 0) + a' 2 if 0 0 (a > 0) V2Tla + iw) otherwise if b 0) V2a sin ax (a > 0) if w| < a; Oif |w| > a 10 х
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a Use t x as a new variable of integration b Use c 3b Then a gives c Repla...View the full answer
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