f(t) = - 4t/T - 2 for -T/2 £ t £ -T/4
f(t) = 4t/T for -T/4 £ t £ T/4
f(t) = - 4t/T + 2 for T/4 £ t £ T/2
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The triangular wave is shown opposite. Because of the discontinuities in
the derivative, then the function has to be expressed as 3 pieces.
These are:- f(t) = - 4t/T - 2 for -T/2 £ t £ -T/4 f(t) = 4t/T for -T/4 £ t £ T/4 f(t) = - 4t/T + 2 for T/4 £ t £ T/2 |
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| Since the Function id odd an = 0 for all n and only the coefficients bn occur in the Fourier Series for f(t). Expression to evaluate bn is shown opposite. |
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| Substituting the Expressions for f(t) into that for bn gives the result Þ |
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| The Expression for bn can be simplified by replacing t with - t in the first integral. This gives Þ |
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| The first 2 integrals contain the term tsinnwt and may be integrated by parts using the result Þ |
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| Evaluating the integrals and using wT = 2p result in the expression opposite for bn. |
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| The triangle wave can now be represented by the Fourier Series Þ. |
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