g(w) = 1 for - W £ w £ + W
and g(w) is zero for all other frequencies.
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A simple example to show the essential steps necessary to find the inverse
transform
f(t)
of
g(w)
is shown in the diagram opposite.
g(w)
can be represented as g(w) = 1 for - W £ w £ + W and g(w) is zero for all other frequencies. |
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| The inverse transform f(t) can be obtained by substituting g(w) into the equation opposite. |
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| After substituting g(w) the expression for f(t) becomes. |
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| When the integral is evaluated and the limits inserted, f(t) reduces to |
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| Furthur Simplification produces the real sinc function multiplied by the area of the pulse/2p. |
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