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The discrete Fourier transform
1992In Chapter 2 we developed properties of the (continuous-time) direct Fourier transform and the inverse Fourier transform, the two constituting an integral pair. Whereas Fourier series analysis is largely concerned with functions which are treated as being periodic, the Fourier transform provides an instrument for the analysis of non-periodic functions.
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2002
The Fourier Transform has wide applications in scientific computing and engineering. Although it has a continuous version, we will consider only the discrete version (DFT) and present what is commonly known as the Fast Fourier Transform (FFT) algorithm.
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The Fourier Transform has wide applications in scientific computing and engineering. Although it has a continuous version, we will consider only the discrete version (DFT) and present what is commonly known as the Fast Fourier Transform (FFT) algorithm.
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The discrete Fourier transform
2003INTRODUCTION From parts 2 and 3 it is obvious that Fourier series and Fourier integrals play an important role in the analysis of continuous-time signals. In many cases we are forced to calculate the Fourier coefficients or the Fourier integral on the basis of a given sampling of the signal.
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Data Transmission by Frequency-Division Multiplexing Using the Discrete Fourier Transform
, 1971B. Weinstein, P. Ebert
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2012
From an analytical perspective, the Fourier series represents a periodic signal as an infinite sum of multiples of the fundamental frequencies, while the Fourier transform permits an aperiodic waveform to be described as an integral sum over a continuous range of frequencies.
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From an analytical perspective, the Fourier series represents a periodic signal as an infinite sum of multiples of the fundamental frequencies, while the Fourier transform permits an aperiodic waveform to be described as an integral sum over a continuous range of frequencies.
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Discrete Fourier Transformation
2015This chapter deals with the discrete Fourier transformation. Here, a periodic series in the time domain is mapped onto a periodic series in the frequency domain. Definitions of the discrete Fourier transformation and its inverse are given. Linearity, convolution, cross-correlation, and autocorrelation are treated as well as Parseval’s theorem.
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Separable data hiding in encrypted image based on compressive sensing and discrete fourier transform
Multimedia tools and applications, 2016Xin Liao, Kaide Li, Jiaojiao Yin
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Concept, implementations and applications of Fourier ptychography
Nature Reviews Physics, 2021Guoan Zheng, Cheng Shen, Shaowei Jiang
exaly