The signum function is given by

\(sgn\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{x}{{\left| x \right|}};x \ne 0}\\ {0;x = 0} \end{array}} \right.\)

The Fourier series expansion of \(sgn\left( {cos\left( t \right)} \right)\) has

1
only sine terms with all harmonics
2
only cosine terms with all harmonies
3
only sine terms with even numbered harmonies.
4
only cosine terms with odd numbered harmonies

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