In Michelson interferometry, many algorithms are used to detect the number of active laser sources at any given time. Conventional FFT-based non-parametric methods are widely used for this purpose. However, non-parametric methods are not the only possible option to distinguish the peaks in a spectrum, as these methods are not the most suitable methods for short data records and for closely spaced wavelengths. This thesis aims to provide solutions to these problems. It puts forward the use of parametric methods such as autoregressive methods and harmonic methods, and proposes two new algorithms to detect the closely spaced peaks for different scenarios of optical signals in wavemeters. Various parametric algorithms are studied, and their performances are compared with non-parametric algorithms for different criteria, e.g. absolute levels, frequency resolution, and accuracy of peak positions. Simulations are performed on synthetic signals produced from specifications provided by our sponsor, i.e., a wavemeter manufacturing company.