A mathematical theory on the computational complexity of the Discrete Fourier Transform (DFT) is required, independently of any kind of known Fast Fourier Transform (FFT) algorithm.

This paper is part 4 in a series of papers about the Discrete Fourier Transform (DFT) and the Inverse Discrete Fourier Transform (IDFT). The focus of this paper is on spectral leakage. Spectral leakage applies to all forms of DFT, including the FFT (Fast Fourier Transform) and the IFFT (Inverse Fast Fourier Transform). We demonstrate an approach to mitigating spectral leakage based on windowing...

Realization of focus Speakers produced words differently in the two focus conditions Acoustic features indicate high word prominence Classification Experiments Discrimination of two focus classes with ~65% correct for individual features (acoustic or visual) Exception f0: 65-83% (depending on speaker) Exception nose features: at chance level Significant AV gain when combining energy and FFT or ...

This paper is part 5 in a series of papers about the Discrete Fourier Transform (DFT) and the Inverse Discrete Fourier Transform (IDFT). The focus of this paper is on the spectrogram. The spectrogram performs a Short-Time Fourier Transform (STFT) in order to estimate the spectrum of a signal as a function of time. The approach requires that each time segment be transformed into the frequency do...

a r t i c l e i n f o a b s t r a c t Keywords: Time–frequency analysis Windowed Fourier transform Wavelet transform Synchrosqueezing Time–frequency representations (TFRs) of signals, such as the windowed Fourier transform (WFT), wavelet transform (WT) and their synchrosqueezed versions (SWFT, SWT), provide powerful analysis tools. Here we present a thorough review of these TFRs, summarizing al...

1. A general criterion for pointwise Fourier inversion 2. Pointwise Fourier inversion on R n (n = 3) 3. Fourier inversion on R 2 4. Fourier inversion on R n (general n) 5. Fourier inversion on spheres 6. Fourier inversion on complex projective space, and variants 7. Fourier inversion on hyperbolic space, and variants 8. Fourier inversion on strongly scattering manifolds 9. Hermite expansions an...

Patients with dysphagia can have higher risks of aspiration after repetitive swallowing activity due to the "fatigue effect". However, it is still unknown how consecutive swallows affect brain activity. Therefore, we sought to investigate differences in swallowing brain networks formed during consecutive swallows using a signal processing on graph approach. Data were collected from 55 healthy p...

A method for the calculation of the fractional Fourier transform (FRT) by means of the fast Fourier transform (FFT) algorithm is presented. The process involves mainly two FFT's in cascade; thus the process has the same complexity as this algorithm. The method is valid for fractional orders varying from -1 to 1. Scaling factors for the FRT and Fresnel diffraction when calculated through the FFT...