f(t) = t/t2 + 1/t for - t £ t £ 0
f(t) = - t/t2 + 1/t for 0 £ t £ + t
and f(t) = 0 for all other values of t.
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The diagram opposite shows an even nonperiodic triangular pulse. The
function f(t) can be written as:- f(t) = t/t2 + 1/t for - t £ t £ 0 f(t) = - t/t2 + 1/t for 0 £ t £ + t and f(t) = 0 for all other values of t. |
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| The Fourier Transform g(w) can be obtained from f(t) by using the standard equation opposite. |
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| Substituting f(t) into the equation for g(w) gives the result:---> |
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| Since t is a constant then the equation for g(w) can be re-expressed as:--> |
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| The integrals can be evaluated using integration by parts. For t e- j w t integration by parts gives the equation opposite. |
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| Carrying out the integration and evaluating the limits results in:--> |
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| After simplification the sinc squared function is obtained as the Fourier transform of a triangular pulse with unit area. Since f(t) is even then g(w) is real. |
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