This paper is part 6 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 correlation. The correlation is performed in the time domain (slow correlation) and in the frequency domain using a Short-Time Fourier Transform (STFT). When the Fourier transform is an FFT, the correlation is said to be a " fast ...

Among the different forms of spectroscopy, nuclear magnetic resonance (NMR) shows an intimate connection between theory and experiment. NMR therefore enjoys great popularity in the development of new methods. Following the rapid development in electronic and computer technology, NMR techniques evolved from singlechannel to multi-channel and multi-dimensional modes. The original continuous wave ...

Carrier-free short pulse widely employed in UWB radar is brought into high-resolution sonar system, which has unique advantages: attaining more target information, restraining fluctuation of reverberation envelop efficiently in short-range detection and achieving accurate estimation. In essence such pulse is transiently short in time domain and wide in frequency domain, and as such it is diffic...

An effective means to approximate an analytic, nonperiodic function on a bounded interval is by using a Fourier series on a larger domain. When constructed appropriately, this so-called Fourier extension is known to converge geometrically fast in the truncation parameter. Unfortunately, computing a Fourier extension requires solving an ill-conditioned linear system, and hence one might expect s...

This work is based on the comparative study of different decomposition methods used to de-noise an ECG signal. There are several signal processing techniques available like Fourier Transform method, Short Term Fourier Transform method, Wavelet analysis, Empirical Mode of Decomposition method etc. Though Fourier Transform method is predominantly used for decomposition purpose but it is not suita...

In order to supply a gap of current resonance vibration and STFT demodulation method applied to rolling bearing fault feature extraction of city rail vehicle, a fault diagnosis method for rolling bearing is presented, which is based on the integration of improved wavelet packet, frequency energy analysis and Hilbert marginal spectrum. When faults occur in rolling bearing, the energy of the roll...

In mixtures of speech signals the energy content of the components of the mixture is important and determine the structure of the mixture. Energy contents of signals are better shown when time-frequency or time-scale planes are used. In this paper we present a comparison of wavelet transform (WT) and short time Fourier Transform (STFT) in spectral analysis of speech signals. We will show in wav...

The notions of time, frequency, and scale are generalized using concepts from unitary operator theory and applied to time-frequency analysis, in particular the wavelet and short-time Fourier transform orthonormal bases and Cohen's class of bi-linear time-frequency distributions. The result is an infinite number of new signal analysis and processing tools that are implemented simply by prewarpin...

The s-transform is a variable window of STFT and extension of wavelet. This paper discussed the principle and method of Wavelet De-noising, reduced noise of pulse signal based on wavelet. It is shown that wavelet de-noising can eliminate most noise, and preserve effectively sudden change of signal. This paper analyzed and compared the effect of denoising of pulse signal in different ways all st...

We study the wavelet transform of functions invariant under a symmetry group, where the wavelet transform is associated to an irreducible unitary group representation. Among other results a new inversion formula and a new covariance principle are derived. As main examples we discuss the continuous wavelet transform and the short time Fourier transform of radially symmetric functions on R. 2000 ...