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 ...

Novel approaches based on windowed Fourier transform for demodulation of fringe patterns were previously presented [Appl. Opt. 43, 2695-2702 (2004)], where extraction of phase and phase derivatives from either phase-shifted fringe patterns or a single-carrier fringe pattern was the main focus. I show that the same methods can be applied to process a single closed-fringe pattern in either noise ...

The windowed Fourier transform of a time signal is considered, as well as a way to reconstruct the signal from a su ciently densely sampled version of its windowed Fourier transform using a Gabor representation; followingGabor, sampling occurs on a two-dimensional time-frequency lattice with equidistant time intervals and equidistant frequency intervals. In the limit of innitely dense sampling,...

anomaly detection (ad) has recently become an important application of target detection in hyperspectral images. the reed-xialoi (rx) is the most widely used ad algorithm that suffers from “small sample size” problem. the best solution for this problem is to use dimensionality reduction (dr) techniques as a pre-processing step for rx detector. using this method not only improves the detection p...

due to its simplicity radix-2 is a popular algorithm to implement fast fourier transform. radix - 2 p algorithms have the same order of computational complexity as higher radices algorithms, but still retain the simplicity of radix-2 . by defining a new concept, twiddle factor template , in this paper we propose a method for exact calculation of multiplicative complexity for radix-2 p algorithm...

Recently several generalizations to higher dimension of the classical Fourier transform (FT) using Clifford geometric algebra have been introduced, including the two-dimensional (2D) Clifford Fourier transform (CFT). Based on the 2D CFT, we establish the two-dimensional Clifford windowed Fourier transform (CWFT). Using the spectral representation of the CFT, we derive several important properti...

When a periodic waveform with a discrete-harmonic spectrum is temporally windowed to make a signal, its spectrum becomes a continuous function of frequency. However, there are discrete-frequency representations for windowed signals such as the Fourier series representation of a periodically extended signal. This article introduces the concept of matching between the temporal window and the peri...