The Fourier Series (FS) and the Discrete Fourier Transform (DFT) should be thought of as playing similar roles for periodic signals in either continuous time (FS) or discrete time (DFT). Both analyze signals into amplitude, phases, and frequencies of complex exponentials; both synthesize signals by linearly combining complex exponentials with appropriate amplitude, phase, and frequency. Finally...

Reliable chemical identification of specific polymers in environmental samples represents a major challenge plastic research, especially with the wide range commercial available, along variable additive mixtures. Thermogravimetric analysis-Fourier transform infrared-gas chromatography-mass spectrometry (TGA-FTIR-GC-MS) offers unique characterization platform that provides both physical and prop...

A method is presented for computing an orthonormal set of eigenvectors for the discrete Fourier transform (DFT). The technique is based on a detailed analysis of the eigenstructure of a special matrix which commutes with the DFT. It is also shown how fractional powers of the DFT can be efficiently computed, and possible applications to multiplexing and transform coding are suggested. T