At first we will explain the required mathematical knowledge which is crucial for the understanding of implemented algorithms in this thesis.
Afterwards we will dive into five different implementations of Fourier transform and analyse their time complexity, number of complex additions and multiplications.
Because of the integration in ALGator system all algorithms will be implemented in Java programming language.
This system is intended to be used by the algorithm developers, because it offers
very convenient implementation, effective testing and fast querying and analysis of the acquired results.
We will compare decimation in time and decimation in frequency implementations of each algorithm and also its iterative and recursive forms.
Testing data on which we will test our algorithms consist of the input data which needs to be transformed and correct transformation result. This way we will be able
to verify the correctness of the algorithms as quickly as possible.