On the Development of STFT-analysis and ISTFT-synthesis Routines and their Practical Implementation

This work introduces the development of two software routines for Short-Time Fourier Transform (STFT) and Inverse Short-Time Fourier Transform (ISTFT) along with know-how about their practical implementation. The proposed algorithms and the corresponding novel Matlab (R) functions form a conjugated analysis-synthesis pair and assist the time-frequency analysis, processing, resynthesis and visualization of real-world non-stationary signals. In the paper, background information is given about the mathematical framework of the STFT, ISTFT and the perfect reconstruction condition. Further, the proposed algorithms and routines are described, based on DFT, IDFT and the overlap-add (OLA) synthesis approach. Comprehensive notes and recommendations are given concerning the applied aspects of their usage. Finally, examples are provided to confirm the consistency of the algorithms and routines, including analysis, spectral modification and resynthesis of non-stationary signals, along with example for the outperformance of the proposed analysis function in comparison with the corresponding in-built Matlab (R) function.