Short-term forecasts (nowcasts) of severe rainfall and flooding are of high importance to the society. In the collaborative adaptive sensing of the atmosphere (CASA) project, a high-resolution X-band radar network was deployed in the Dallas-Fort Worth (DFW) urban area. The dynamic and adaptive radar tracking of storms (DARTS) is a key component of the precipitation nowcasting system that was developed in the CASA project. In DARTS, the advection field determination is formulated in the spectral domain using the discrete Fourier transform (DFT). Building on the earlier work, an extension of DARTS is proposed. The novelty of the proposed scale filtering (SF-DARTS) method is the formulation of the extrapolation also in the spectral domain. The extrapolation method is combined with autoregressive AR(2) models applied to Fourier frequency bands together with adaptive truncation of DFT coefficients. This effectively filters small spatial scales having low predictability. It is shown that the proposed approach improves forecast skill and gives improved computational efficiency compared to conventional methods. Another important contribution is that DARTS is being evaluated for the first time beyond the urban scale. DARTS and SF-DARTS are evaluated using data from two different sources, namely the urban-scale CASA DFW network (200 km), and the country-wide radar network operated by the Finnish Meteorological Institute (1000 km).