Estimation of pseudo-periodic signals

Many phenomena exhibit cyclical patterns without being periodic. This can be modeled using "pseudo-periodic" functions which enable cyclical patterns to be decomposed into a periodic signal along with a set of parameters that define the deviations of the pattern from true periodicity. This paper describes algorithms that estimate the parameters and the template function using the p-norm cost function. Implementation issues such as varying amplitude between pseudoperiods and problems using finite data records are also discussed. Applications to sunspot data explore practical uses and limitations of the method.