Chapter 1 The Fourier Transform
discontinuity, just as for Fourier series. 2. A truncated cosine wave. f(t) = 8 <: cos3t if ˇ<t<ˇ 1 2 if t= ˇ 0 otherwise: Then, since the cosine is an even function, we have f^( ) = p 2ˇF[f]( ) = Z 1 1 f(t)e i tdt= Z ˇ ˇ cos(3t)cos( t)dt = 2 sin( ˇ) 9 2: 5
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