(a) Show that if f(x) has a Fourier transform, so does f(x - α), and F{f(x - α)} = e^-iwαF{f(x)}.

(b) Using (a), obtain formula 1 in Table III, from formula 2.

(c) Show that if f̂(w) is the Fourier transform of f(x), then f̂(w - α) is the Fourier transform of e^iαxf(x).

(d) Using (c), obtain formula 7 in Table III from 1 and formula 8 from 2.

Transcribed Image Text:

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