Nowadays fast and precise signal processing is becoming more and more important. One of the main focus is on measuring the spectral components of the investigated signal. The recursive variant of discrete Fourier transform offers for this aim a good solution. RDFT's advantage is its robustness and the efficient realization on FPGA. But this procedure is built up with fixed structure of resonators, which can cause spectral leakage and picket fence effects, if the signal's frequency component is not the same grid as of the RDFT. To eliminate this problem the adaptive Fourier analysis is a useful tool, that can build up a variable structure depending on signal.
The use of these methods is beneficial in practical applications. Today it is more and more important to transmit with higher data rate over the available frequencies bands. Orthogonal frequency-division multiplexing (OFDM) uses a large number of digital modulated subcarriers to transmit the data. The modulation is performed by inverse Fourier transform and after digital to analog conversion the signal is converted to the carrier band. At the receiver side the process is the similar, the demodulation of the subcarriers is done by use of Fourier transform. Many errors can occurs in the transmission change. In my thesis I investigated the frequency offset error between the transmitter and receiver local oscillators. Especially in OFDM-systems if these frequencies are not the same, intercarrier interference will occur.
In my thesis I discussed these two topics. First of all I investigate this technologies through self made simulations. Secondly, I study the OFDM-system and its performance in presence of additive noise and frequency offset.