Short-time fourier transform STFT

In most STSA techniques the short-time analysis of the signal is performed by use of the Short-Time Fourier Transform (STFT) [Lim and Oppenheim, 1979, Boll, 1991, Ephraim and Malah, 1984, Moorer and Berger, 1986], or with a uniform filter-bank that can be implemented by STFT [Sondhi et al., 1981, Vary, 1985, Lagadec and Pelloni, 1983], Note that in such cases the two interpretations (multirate filter-... 

The Phase Vocoder. The Phase Vocoder [Flanagan and Golden, 1966][Gordon and Strawn, 1985] is a common analysis technique because it provides an extremely flexible method of spectral modification. The phase vocoder models the signal as a bank of equally spaced bandpass filters with magnitude and phase outputs from each band. Portnoff s implementation of the Short Time Fourier Transform (STFT) provides a time-efficient implementation of the Phase Vocoder. The STFT requires a fast implementation of the Fast Fourier Transform (FFT), which typically involves bit addressed arithmetic. 

An analysis/synthesis system based on a filter bank representation of the signal can be derived from the time-dependent short-time Fourier transform (STFT) [Nawab and Quatieri, 1988a]... 

Looking at Figure 9.36, it is obvious that the signal could be represented by only one or two frequency components if the transformation was performed within a moving time window. This kind of time-frequency analysis is available in the so-called short-time Fourier transform (STFT). The problem with STFT is that the resolution in time and... 

Some of the commonly used algorithms for time-frequency representations of spectral estimates include the short-time Fourier transform (STFT), the Wigner-Ville transform, wavelet transforms, etc. A good summary of the mathematical basis of each of these techniques can be found in Ref. 11. 

The resultant transform is named short-time Fourier transform (STFT). 

Keywords— Gastrostomy, Gastroesophageal reflux disease (GERD), Electrogastrography (EGG), Heart rate variability (HRV), Short-time Fourier transform (STFT). 

Some of the methods used in TED are short time Fourier transform (STFT), wavelet transform (WT) and wavelet packet transform (WPT). In general, the difference between these methods is the partitioning of the time-scale axis. In short-time Fourier transform (STFT), the EMG signal is mapped into frequency components that present within an interval of time (window). A suitable window size must be determined prior to this as small window will give good time resolution but poor frequency resolution and vice versa. The partitioning ratio of the STFT is fixed once specified, each cell has an identical aspect ratio. To overcome the resolution problem in STFT, WT was developed. 

To address the aforementioned issues of ICA, it is proposed by Yang and Nagarajaiah (2013a) to transform the time-domain modal expansion Eq. 11 to the time-frequency domain where the target modal responses have sparse representations, using the short-time Fourier transform (STFT) prior to the ICA estimation. 

Suppression rules. Let X(p,Qk) denote the short-time Fourier transform of x[ri, where p is the time index, and Qk the normalized frequency index (0t lies between 0 and 1 and takes N discrete values for k = 1,N, Wbeing the number of sub-bands). Note that the time index p usually refers to a sampling rate lower than the initial signal sampling rate (for the STFT, the down-sampling factor is equal to hop-size between to consecutive short-time frames) [Crochiere and Rabiner, 1983]. 

The most widespread opinion is that the phase need not be modified because of the properties of the human auditory system [Lim and Oppenheim, 1979]. Strictly speaking however, the assertion that the ear is insensitive to the phase was highlighted by psychoacoustic findings only in the case of stationary sounds and for the phase of the Fourier transform [Moore, 1997]. Moreover, it is well known that in the case of STFT, phase variations between successive short-time frames can give rise to audible effects (such as frequency modulation) [Vary, 1985]. 

The STFT thus results in a spectrum that depends on the time instant to which the window is shifted. The choice of Gaussian functions for the short-duration window gives excellent localization properties despite the fact that the functions are not limited in time. Alternatively, STFT can also be viewed as filtering the signal at all times using a bandpass filter centered around a given frequency/whose impulse response is the Fourier transform of the short-duration window modulated to that frequency. However, the duration and bandwidth of the window remain the same for all frequencies. 

---