In this paper Adaptive Chirp transform (ACT) and Chirp-z transform (CZT) for measurements of frequency spectrum are presented. Algorithms are adjusted according to IEC 61000-4-7 standard. Interpolated ACT with narrowed frequency span is used for Phase Lock Loop (PLL) synchronization. The CZT is used along with windows function, to obtain the amplitudes of signal harmonics and interharmonics. Window function length is defined by PLL. All parts of proposed algorithm are tested through various simulations with changing parameters of analysed signals. This paper shows that CZT can be adjusted to synchronization and measurement of frequency spectrum. Results are comparable to the traditional approach (DFT) and completely satisfy the needs according to standard IEC 61000-4-7.