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Showing papers on "Discrete-time Fourier transform published in 2019"


Journal ArticleDOI
TL;DR: It is shown how spectral filters can improve the convergence of numerical schemes which use discrete Hilbert transforms based on a sinc function expansion, and thus ultimately on the fast Fourier transform.
Abstract: We show how spectral filters can improve the convergence of numerical schemes which use discrete Hilbert transforms based on a sinc function expansion, and thus ultimately on the fast Fourier transform. This is relevant, for example, for the computation of fluctuation identities, which give the distribution of the maximum or the minimum of a random path, or the joint distribution at maturity with the extrema staying below or above barriers. We use as examples the methods by Feng and Linetsky (Math Finance 18(3):337–384, 2008) and Fusai et al. (Eur J Oper Res 251(4):124–134, 2016) to price discretely monitored barrier options where the underlying asset price is modelled by an exponential Levy process. Both methods show exponential convergence with respect to the number of grid points in most cases, but are limited to polynomial convergence under certain conditions. We relate these rates of convergence to the Gibbs phenomenon for Fourier transforms and achieve improved results with spectral filtering.

18 citations


Journal ArticleDOI
TL;DR: The computational complexities of the resulting FFT algorithms are analyzed, that exploits the structure of the suggested multiple rank-1 lattice spatial discretizations, in detail and obtain upper bounds in O ( M log ⁡ M ) , where the constants depend only linearly on the spatial dimension.

16 citations


Journal ArticleDOI
TL;DR: An efficient and automated experimental platform for frequency modulated continuous wave (FMCW) radars that integrates a programmable transmitter based on field programmable gate array and a discrete-time Fourier transform to process low-frequency signals.
Abstract: This paper proposes a design of an efficient and automated experimental platform for frequency modulated continuous wave (FMCW) radars. The platform can quickly flexibly generate the waveform that meets measurement requirements and significantly improve experimental efficiency.,This platform not only includes radio frequency devices but also integrates a programmable transmitter based on field programmable gate array. By configuring the waveform data, the experimental platform can generate waveforms with adjustable parameters and realize automatic emission, reception and processing of signals. Different from traditional fast Fourier transform, this paper uses a discrete-time Fourier transform to process low-frequency signals to get more accurate results.,The authors demonstrate the effectiveness of the platform through a single-path cable experiment, an indoor ranging experiment by using different modulating waveforms and a speed measurement experiment. With complete functions and strong flexibility, the platform can operate effectively in various conditions and greatly improve the efficiency of research and study.,The platform can accelerate the research studies and applications of FMCW radars in the fields of automatic drive, through-wall detection and health-care applications.,Cost and functionality are taken into account in the platform, which can significantly improve the efficiency of research. The proposed signal processing method improves the accuracy while its computation complexity does not increase significantly.

4 citations


Proceedings ArticleDOI
01 Jan 2019
TL;DR: The paper addresses general issues related to signal analysis with Fourier transform in the context of electrotechnical tasks and detailed description of relation among continuous Fouriertransform, discrete-time Fourier Transform (DTFT), and discrete Fourier transforms (DFT) is provided.
Abstract: The paper addresses general issues related to signal analysis with Fourier transform in the context of electrotechnical tasks. A detailed description of relation among continuous Fourier transform, discrete-time Fourier transform (DTFT), and discrete Fourier transform (DFT) is provided. DFT frequency resolution increase methods are compared. Analysis algorithm of DFT results is provided. The algorithm allows increasing the accuracy of identifying harmonic composition of a signal and also revealing closely spaced harmonics that substantially differ in amplitudes.

3 citations


Journal ArticleDOI
TL;DR: In this article, the authors used Discrete-time Fourier Transform (DTFT), Wavelet transform (WT) and Wiener transform (WT) to detect damage in concrete gravity dams.
Abstract: In structural engineering, damage detection in concrete gravity dams (CGDS) is a practical problem. Dam destruction can have severe financial consequences and may even lead to fatalities. Therefore, structural health monitoring in advance is crucial. In this regard, a well-known CGD, namely the Pine Flat Dam, has been chosen for the Finite Element Modeling. In this paper, damage is induced in the dam neck through elasticity modulus reduction by 40 % and 80 %. In addition, after applying Northridge earthquake, the acceleration in structure nodes for intact and damaged cases are recorded in vector formats. Using various methods, such as Discrete-time Fourier Transform (DTFT), Wavelet transform and Wiener transform, the differences between these two signals are investigated. The standard deviation (S.D.) of variations is chosen as the performance metric and is applied to the signal amplitude between intact and damage observations/signals. The reason why several signal processing algorithms are used is finding an approach which shows more clearly the differences caused by the destruction. This is evaluated via S.D. values for different algorithms. The results confirm the superiority of DTFT over other given algorithms. DTFT has a negligible outperformance (approximately zero dB) with respect to the Wavelet transform in both the crest and the lower nodes of the dam. This rate for DTFT and Wavelet is 10dB higher than that of Wiener and 35 dB in comparison with the simple amplitude difference. Moreover, the detection thresholds for the given methods are compared, and it is verified that the DTFT and Wavelet indicate the best performance.

2 citations


Book ChapterDOI
17 Feb 2019
TL;DR: The paper studies the performance of the proposed method and compares it to other estimation techniques such as root-multiple signal classification (root-MUSIC) and the discrete-time Fourier transform (DTFT).
Abstract: This work investigates a new approach for frequency estimation of multiple complex sinusoids in the presence of noise. The algorithm is based on the optimization of the least squares (LS) cost function using a gradient ascent algorithm. The paper studies the performance of the proposed method and compares it to other estimation techniques such as root-multiple signal classification (root-MUSIC) and the discrete-time Fourier transform (DTFT). Simulation results show the performance gains provided by the proposed algorithm in different scenarios.

2 citations


Proceedings ArticleDOI
01 Sep 2019
TL;DR: The accuracies - as expressed by the Total Vector Error - of the proposed fast-Twls algorithm and the real-valued TWLS algorithm recently proposed in the literature are compared to each other under several static and dynamic testing conditions suggested in the IEEE Standard C37.118.1-2011 for synchrophasor measurements for power systems.
Abstract: This paper proposes a fast Taylor Weighted Least Squares (fast-TWLS) algorithm for accurate real-time synchrophasor estimation. It requires the calculation at runtime of only two Discrete Time Fourier Transforms (DTFTs) at nominal frequency and further few elementary arithmetic operations. The accuracies - as expressed by the Total Vector Error (TVE) - of the proposed fast-Twls algorithm and the real-valued TWLS algorithm recently proposed in the literature are compared to each other under several static and dynamic testing conditions suggested in the IEEE Standard C37.118.1-2011 for synchrophasor measurements for power systems.

1 citations


Journal ArticleDOI
TL;DR: In this paper, the authors proposed the Golden Angle Linogram Fourier Domain (GALFD) to estimate the Discrete-Time Fourier Transform (DTFT) at points of a finite domain.
Abstract: Estimation of the Discrete-Time Fourier Transform (DTFT) at points of a finite domain arises in many imaging applications. A new approach to this task, the Golden Angle Linogram Fourier Domain (GALFD), is presented, together with a computationally fast and accurate tool, named Golden Angle Linogram Evaluation (GALE), for approximating the DTFT at points of a GALFD. A GALFD resembles a Linogram Fourier Domain (LFD), which is efficient and accurate. A limitation of linograms is that embedding an LFD into a larger one requires many extra points, at least doubling the domain's cardinality. The GALFD, on the other hand, allows for incremental inclusion of relatively few data points. Approximation error bounds and floating point operations counts are presented to show that GALE computes accurately and efficiently the DTFT at the points of a GALFD. The ability to extend the data collection in small increments is beneficial in applications such as Magnetic Resonance Imaging. Experiments for simulated and for real-world data are presented to substantiate the theoretical claims. The mathematical analysis, algorithms, and software developed in the paper are equally suitable to other angular distributions of rays and therefore we bring the benefits of linograms to arbitrary radial patterns.

1 citations


Proceedings ArticleDOI
01 May 2019
TL;DR: This paper investigates the accuracies of the sine-wave amplitude and phase estimators provided by an enhanced Frequency-domain Linear Least-Squares (e-FLLS) algorithm and the classical three-parameter sin-fit (3PSF) method, and the weighted three- parameter sine -fit (W3PSf) algorithm are compared each other through both theoretical and simulation results.
Abstract: This paper investigates the accuracies of the sine-wave amplitude and phase estimators provided by an enhanced Frequency-domain Linear Least-Squares (e-FLLS) algorithm recently proposed in the literature. The e-FLLS algorithm adopts the rectangular window and it considers three Discrete Time Fourier Transform (DTFT) samples to compensate the contribution of the spectral image component. Analytical expressions for the Mean Squares Errors (MSEs) of the e-FLLS amplitude and phase estimators are derived and their accuracies are verified by means of computer simulations. Moreover, the accuracies of the amplitude and phase estimators provided by the e-FLLS algorithm, the classical three-parameter sine-fit (3PSF) method, and the weighted three-parameter sine-fit (W3PSF) algorithm are compared each other through both theoretical and simulation results.

1 citations


Journal ArticleDOI
TL;DR: The mathematical analysis, algorithms, and software developed in the paper are equally suitable to other angular distributions of rays and therefore the benefits of linograms are brought to arbitrary radial patterns.
Abstract: Estimation of the Discrete-Time Fourier Transform (DTFT) at points of a finite domain arises in many imaging applications. A new approach to this task, the Golden Angle Linogram Fourier Domain (GALFD), is presented, together with a computationally fast and accurate tool, named Golden Angle Linogram Evaluation (GALE), for approximating the DTFT at points of a GALFD. A GALFD resembles a Linogram Fourier Domain (LFD), which is efficient and accurate. A limitation of linograms is that embedding an LFD into a larger one requires many extra points, at least doubling the domain's cardinality. The GALFD, on the other hand, allows for incremental inclusion of relatively few data points. Approximation error bounds and floating point operations counts are presented to show that GALE computes accurately and efficiently the DTFT at the points of a GALFD. The ability to extend the data collection in small increments is beneficial in applications such as Magnetic Resonance Imaging. Experiments for simulated and for real-world data are presented to substantiate the theoretical claims. The mathematical analysis, algorithms, and software developed in the paper are equally suitable to other angular distributions of rays and therefore we bring the benefits of linograms to arbitrary radial patterns.

1 citations


Book ChapterDOI
01 Jan 2019
TL;DR: In this article, the computational complexity of computing an N-point discrete-time Fourier transform (DFT) using a brute-force method is evaluated. But the complexity is not shown in this paper.
Abstract: As was defined in a previous chapter, the discrete Fourier transform (DFT) is the sampled version of the discrete-time Fourier transform (DTFT), with a finite number of samples taken around the unit circle in the Z-domain. DFT is very useful in the analysis of discrete-time signals and linear time-invariant discrete-time systems. It is, therefore, necessary to determine the computational complexity in performing an N-point DFT of a sequence so that we may be able to come up with a more efficient computational algorithm. To this end, let us first evaluate the computational complexity of computing an N-point DFT using brute-force method. Consider an N-point discrete-time sequence {x[n]}, 0 ≤ n ≤ N − 1, N ∈ Z. Its DFT is given by

Book ChapterDOI
01 Jan 2019
TL;DR: Since periodic discrete-time signals have a periodic and discrete-frequency transform the Fourier series is a special case of the DFT, which in turn is implemented very efficiently by the Fast Fourier Transform (FFT) algorithm.
Abstract: If the Z-transform of a signal or the transfer function of a system is defined on the unit circle then the Discrete-Time Fourier Transform (DTFT) of the signal or the frequency response of the system are obtained. Two computational disadvantages of the DTFT, being a function of a continuously varying frequency and requiring integration for the inversion, are removed by sampling in frequency and resulting in the Discrete Fourier Transform (DFT). Since periodic discrete-time signals have a periodic and discrete-frequency transform the Fourier series is a special case of the DFT. Circular representation, circular shift and circular convolution characterize the DFT. Thus, periodic or aperiodic signals can be represented and processed by the DFT, which in turn is implemented very efficiently by the Fast Fourier Transform (FFT) algorithm. Basic theory and application of the FFT are introduced. Fourier representation and processing of two-dimensional signals and systems are similar to those in one dimension. The use of transforms for data compression is illustrated by the discrete cosine transform, which represents the signal efficiently using real-valued coefficients. MATLAB is used for computation of the transforms and processing of one- and two-dimensional signals.

Book ChapterDOI
01 Jan 2019
TL;DR: There is an efficient algorithm known as the fast Fourier transform (FFT) to perform filtering of long sequences, power spectrum estimation, and related tasks and this chapter will learn about the FFT.
Abstract: Discrete Fourier transform (DFT) is a frequency domain representation of finite-length discrete-time signals. It is also used to represent FIR discrete-time systems in the frequency domain. As the name implies, DFT is a discrete set of frequency samples uniformly distributed around the unit circle in the complex frequency plane that characterizes a discrete-time sequence of finite duration. DFT is also intrinsically related to the DTFT, as we will see in this chapter. Because DFT is a finite set of frequency samples, it is a computational tool to perform filtering and related operations. There is an efficient algorithm known as the fast Fourier transform (FFT) to perform filtering of long sequences, power spectrum estimation, and related tasks. We will learn about the FFT in this chapter as well.

Patent
15 Feb 2019
TL;DR: In this paper, the authors proposed an analyzing method for heart rate variability based on a linear amplitude spectrum, which is reasonable in design, a time domain signal is transformed into the frequency domain, and through linear spectrum transform, the amplitude of the signal reflects the real amplitude in the signal time domain; the significant physiological significance is achieved on analyzing frequency and intensity of regulating HRV by the sympathia-parasympathetic nerve through the calculated frequency domain parameters.
Abstract: The invention relates to an analyzing method for heart rate variability based on a linear amplitude spectrum. The method comprises the following steps that a target heart rate variability signal is resampled, and a uniform time interval sequence is obtained; discrete time Fourier transform is conducted on the uniform time interval sequence; according to the discrete time Fourier transform, the linear amplitude spectrum is calculated and obtained; according to the linear amplitude spectrum, data points in an extreme low-frequency stage, a low-frequency stage, a high-frequency stage and a totalfrequency stage are summed, and five analyzed parameters of the heart rate variability frequency-domain, such as an extreme low-frequency amplitude parameter, a low-frequency amplitude parameter, a high-frequency amplitude parameter, a total amplitude parameter and a balance specific parameter are calculated. The analyzing method is reasonable in design, a time domain signal is transformed into the frequency domain, and through linear amplitude spectrum transform, the frequency domain amplitude of the signal reflects the real amplitude in the signal time domain; the frequency domain characteristic is used for analyzing of physiological signals of HRV and the like, and the significant physiological significance is achieved on analyzing frequency and intensity of regulating HRV by the sympathia-parasympathetic nerve through the calculated frequency domain parameters.

Book ChapterDOI
25 Mar 2019
TL;DR: A general use tool is developed for the frequency analysis that achieves execution times in a linear relation with the length of the vector to be processed and the number of samples required.
Abstract: A method for the calculation of spectrum samples of discrete, aperiodic and finite signals based on the DTFT is proposed. This method is based on a flexible discretization of the frequency variable that could produce equidistant, sparse or unique spectrum samples. It is implemented in a GPU platform as a Matrix-Vector product, being able to be applied on modern HPC systems. As a result, a general use tool is developed for the frequency analysis that achieves execution times in a linear relation with the length of the vector to be processed and the number of samples required. Finally, it is shown that the required execution time for the computation of equally spaced spectrum samples is competitive to the achievements of other tools for frequency analysis based on sequential execution.

Journal ArticleDOI
01 Apr 2019
TL;DR: An application GUI (Graphical User Interface) is designed as a software simulation to compare the output signal of DFT and DTFT, part of the digital signal processing.
Abstract: An application GUI (Graphical User Interface) is designed as a software simulation to compare the output signal of DFT and DTFT. DFT (Discrete Fourier Transform) and DTFT (Discrete Time Fourier Transform) are part of the digital signal processing. Digital signal processing is an analog signal processing method uses a mathematical technique to perform a transformation or retrieving information in digital form. One of the benefits of digital signal processing is to facilitate the representation of the signal, because the signal in digital form will be more visible, easily processed and has high accuracy. This GUI application designed using LabVIEW from National Instruments. LabVIEW is a software graphical programming or a block diagram. LabVIEW program known as VI or Virtual Instrument. The input signal in this application is a square signal

Book ChapterDOI
01 Jan 2019
TL;DR: A mapping known as the discrete-time Fourier transform that characterizes discrete- time signals and systems in the frequency domain is defined and the relationship between the Z-transform and DTFT is shown.
Abstract: Signals, continuous-time, or discrete-time occur in the time domain. We, therefore, described rather elaborately discrete-time signals and systems in the time domain. For easier and more efficient ways to analyze such signals and systems, we next introduced the Z-transform, which is an alternative representation of discrete-time signals and systems. The Z-transform maps a discrete-time signal or an LTI discrete-time system from the discrete-time domain into a complex plane. In this plane, the discrete-time signals and systems are represented by their poles and zeros. There is another domain in which a discrete-time signal or equivalently an LTI discrete-time system can be represented. This domain is the frequency domain. We can visualize a signal more easily in the frequency domain than in the time domain. For instance, a sum of sinusoidal signals with differing frequencies is hard to identify in the time domain individually. On the other hand, such a signal can be easily identified individually in the frequency domain. This is illustrated in Figs. 4.1a and b. The discrete-time signal is shown in Fig. 4.1a. It consists of three sinusoids at frequencies 13, 57, and 93 Hz with amplitudes 1, 1.5, and 2, respectively, at a sampling frequency of 500 Hz. It is hard to discern the individual sinusoids from the figure. Figure 4.1b shows the discrete-time Fourier transform (DTFT) representation of the signal in Fig. 4.1a. One can clearly distinguish the three components in frequency and relative amplitude. The DTFT also greatly aids in the design of LTI discrete-time systems. This chapter deals with the representation of discrete-time signals and systems in the frequency domain. More specifically, we will define a mapping known as the discrete-time Fourier transform that characterizes discrete-time signals and systems in the frequency domain. As a consequence, we will show the relationship between the Z-transform and DTFT. We will also observe that the DTFT characterizes an LTI discrete-time system in the frequency domain. Because of this property, we can define the filtering operations. Filters such as lowpass, highpass, bandpass, bandstop, etc., can be characterized more efficiently in the frequency domain. It further leads us to the design of such filters (Tables 4.1, 4.2 and 4.3).