Function f(t). Fourier Transform
f(t)e. ?j2?st dt. The inverse Fourier transform transforms a func- f(t) = e. ?? t. 2 . By the definition of Fourier transform we see.
(e.g. x(t) and X(?)
Mar 1 2010 2. Example 1 Find the Fourier transform of f(t) = exp(?
= -sm -w . w. 2. 2. With f(t) = e-t2 the Fourier transform is.
'The double-sided exponential function is shown. The Fourier transform of the single-sided exponen- tial f(t) = exp(-t) with t 2 0
Find the Fourier transform of the signal x(t) = { 1. 2. 1. 2 ?
e. ?t sin t t. } . Using the first shift theorem (Theorem 1.2) and the result of Exercise 2 above yields the result that the required Laplace transform is
x(?)e?j(?n)w0? d? = C?n. Page 9. 106 • Basic System Analysis. Example 8: Compute the exponential series of the following signal. ?5 ?4 ?3 ?2 ?1 0. 1. T.