Consider the function f(t) below, which is a cosine within the time interval -t/2 to +t/2 and zero elsewhere.

The applet below shows the Fourier transform of a time limited sinusoid.

Fn = 1 shows a time limited sine width t and frequency wo.

The odd spectrum is in pink.

Fn = 2 to 7 show special cases of Fn = 1.

Fn = 8 shows a time limited cosine.

Fn = 9 to 13 show special cases of Fn = 8.

Fn = 14 shows a time limited sinusoid which can be changed from sine to cosine by Ph.

Fn = 15 to 17 show special cases of Fn = 14.

Fn = 18 shows a time limited sine with edges modified by a triangle.

Fn = 19 to 23 show special cases of Fn = 18.

Fn = 24 shows a time limited cosine with edges modified by a triangle.

Fn = 25 to 29 show special cases of Fn = 24.

27 and 28 are shown with several values wo.

of t.

29 is shown with several values of Fn = 30 shows a time limited sinusoid which can be changed from sine to cosine and with edges modified by a triangle.

Fn = 31 to 33 show special cases of Fn = 30.

Fn = 34 shows a time limited sine with edges modified by a raised cosine.

Fn = 35 to 41 show special cases of Fn = 34.

Fn = 42 shows a time limited cosine with edges modified by a raised cosine.

Fn = 43 shows a special case of Fn = 42.

Fn = 44 shows a time limited sinusoid which can be changed from sine to cosine and with edges modified by a raised cosine.

Fn = 45 shows a special cases of Fn = 44.

Fn = 46 shows a time limited cosine being reconstructed from its spectrum.

Fn = 47 to 51 show special cases of Fn = 46.

Fn = 52 shows a time limited cosine with triangle edge being reconstructed from its spectrum.

Fn = 53 to 56 show special cases of Fn = 52.

COPYRIGHT © 1996, 2012 Cuthbert Nyack.