The aim of the study was to identify and compute oscillations in two different time series with similar amplitude variations using length of day data with tide model removed (LODR) and total solar irradiance (TSI) data. The combination of the Fourier transform band pass filter and Hilbert transform allows to detect amplitude variations as a function of oscillation period. Amplitude variations in two different time series enable computation of frequency dependent or time-frequency correlation coefficients between them. It allows also to identify such oscillations in two time series which have similar amplitude variations. The method applied to LODR and TSI data, enable to detect possible relationship between them. This comparison method can be applied to any time series which consist of oscillations with non-constant amplitudes.