Fabian Renn's visualisation of Time-Varying Discrete Fourier-Transforms

By Fabian Renn

This is an implementation of a TV-DFT (Time-Varying Discrete Fourier Transform). The Discrete Fourier-Transform is a technique to analyse the harmonic content of a signal and is used in many areas of science and engineering. For example, the MP3 codec heavily relies on the DFT. However, the traditional DFT requires a fare amount of computer memory, as the whole signal of interest must reside in computer memory. Therefore, the traditional DFT is not always feasible when analysing large simulation results. The TV-DFT, on the other hand, does not need to store all of the previous time-steps and is computationally far less demanding. The down side is that it only calculates a single Fourier coefficient F(ω₀) for every time step. The TV-DFT is basically a digital bandwidth filter tuned to the frequency ω, followed by a de-modulation step. The filter is implemented with a recursive filter design which makes use of the z-Transform. This way, by only saving 3 previous time steps, a decent TV-DFT can be constructed.