Topic
Discrete Fourier transform
About: Discrete Fourier transform is a research topic. Over the lifetime, 10234 publications have been published within this topic receiving 207520 citations.
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01 Jan 2018
TL;DR: This chapter summarizes the least-squares error solutions and minimum-norm solutions of linear equations and aids understanding the sampling theorem in a more intuitive manner.
Abstract: Signal analysis of discrete sequences is formulated using linear equations. This chapter summarizes the least-squares error solutions and minimum-norm solutions of linear equations. Linear and orthogonal regression analyses are in particular significant topics in discrete signal analysis in the time domain. Signal detection or source signal separation provides a good example that gives an intuitive understanding of regression analysis. Orthogonality or decorrelation is the basic notion underscoring the theoretical tools of discrete signal analysis. The Fourier transform of a sequence provides the spectral representation of the sequence based on the orthogonality of sinusoidal functions; however, the discrete Fourier transform yields the discrete spectral sequence that represents a periodic discrete sequence based on the orthogonality of vectors. The discrete Fourier transform is a practical way to discretize the signal representation. In addition to this discretization, it aids understanding the sampling theorem in a more intuitive manner.
TL;DR: In this paper, the authors derived an equivalent circuit of an orthogonal function type ADF using the latter pole location, in which phase of a pole of a resonator of a frequency sampling filter is shifted by π/N(rad).
Abstract: An orthogonal function-type adaptive digital filter (orthogonal function type ADF) is known as a means of improving the convergence speed of a tap coefficient in the case in which input is a colored signal such as a voice. Two different methods have been used for pole location of a transfer function of this ADF. One is the pole location of equal interval of 2π/N(rad). (N: tap number of ADF) starting at the phase 0 (rad) on the circle whose radius is very close to 1 within the unit circle of the z-plane. The other is the one resulting from rotating the above location by π/N(rad). In the case of the former pole location, it has been shown that it is equivalent to a frequency sampling type ADF such that input is a periodic process of period N. Why improvement in convergence speed of the latter is the case is not clear at this date.
In this paper we first derive an equivalent circuit of an orthogonal function type ADF using the latter pole location. In this circuit a modified discrete Fourier transform (MDFT) appears in which phase of a pole of a resonator of frequency sampling filter is shifted by π/N(rad). Next, we present a condition for expansion coefficients of the MDFT circuit to be orthogonal to one another. Moreover, we clarify that this equivalent circuit is of a construction that satisfies the orthogonal condition of the MDFT circuit. Finally, we verify these results of investigation by several computer simulations.
TL;DR: In this article, a method for obtaining the two-dimensional transform of an image from a finite number of one-dimensional cross sections is described, where the transform is obtained from a fixed number of cross sections.
Abstract: A method for obtaining the two-dimensional transform of an image from a finite number of one-dimensional cross sections is described.
01 Jan 2015
TL;DR: The study of Fourier transform, its strength and limitations, is the starting point of the journey to the wavelets.
Abstract: In order to devise good representation techniques we must develop tools that enable us to locate distinguished features of a function. The most traditional of these tools is the Fourier Transform which we will study in this chapter. The study of Fourier transform, its strength and limitations, is the starting point of our journey to the wavelets.
01 Aug 2021
TL;DR: In this paper, the average block error rate (BLER) performance of circular 256QAM schemes considering a peak-to-average power ratio measure called a cubic metric (CM) for discrete Fourier transform (DFT)-precoded OFDM in multipath fading channels was analyzed.
Abstract: This paper presents the average block error rate (BLER) performance of circular 256QAM schemes considering a peak-to-average power ratio measure called a cubic metric (CM) for discrete Fourier transform (DFT)-precoded orthogonal frequency division multiplexing (OFDM) in multipath fading channels. Computer simulation results show that the required average received signal-to-noise power ratio (SNR) satisfying the average BLER of 10−2 considering the CM for the (16×16) circular 256QAM constellation is deceased by approximately 0.5 dB, and that for the (32×8) and (64×4) circular 256QAM constellations is deceased by approximately 0.3 dB compared to the rectangular 256QAM scheme when using reference signal (RS) based channel estimation. Therefore, we conclude that the circular 256QAM constellation with independent bit mapping to either the phase or amplitude information is effective in achieving a lower required average received SNR satisfying the target average BLER than that for rectangular 256QAM considering the CM in multipath fading channels.