Showing papers on "Discrete-time Fourier transform published in 2021"

The Generalized Fourier Transform: A Unified Framework for the Fourier, Laplace, Mellin and Z Transforms.

Abstract: This paper introduces Generalized Fourier transform (GFT) that is an extension or the generalization of the Fourier transform (FT). The Unilateral Laplace transform (LT) is observed to be the special case of GFT. GFT, as proposed in this work, contributes significantly to the scholarly literature. There are many salient contribution of this work. Firstly, GFT is applicable to a much larger class of signals, some of which cannot be analyzed with FT and LT. For example, we have shown the applicability of GFT on the polynomially decaying functions and super exponentials. Secondly, we demonstrate the efficacy of GFT in solving the initial value problems (IVPs). Thirdly, the generalization presented for FT is extended for other integral transforms with examples shown for wavelet transform and cosine transform. Likewise, generalized Gamma function is also presented. One interesting application of GFT is the computation of generalized moments, for the otherwise non-finite moments, of any random variable such as the Cauchy random variable. Fourthly, we introduce Fourier scale transform (FST) that utilizes GFT with the topological isomorphism of an exponential map. Lastly, we propose Generalized Discrete-Time Fourier transform (GDTFT). The DTFT and unilateral $z$-transform are shown to be the special cases of the proposed GDTFT. The properties of GFT and GDTFT have also been discussed.

Unbiased Sine-wave Frequency Estimation by Parabolic Interpolation of DTFT Samples

Abstract: In this paper the Parabolic Interpolated Discrete-Time Fourier Transform (PIpDTFT) algorithm proposed for the frequency estimation of a complex-valued sine-wave is extended to signal weighted by a Maximum Sidelobe Decay (MSD) window and its accuracy is analyzed. A criterion is proposed that enables the determination of the maximum distance between the DTFT interpolation points that ensures a negligible estimator bias. Also, the accuracy of the PIpDTFT frequency estimator is analyzed as a function of the accuracy of the used initial frequency estimate. Moreover, the robustness of the PIpDTFT frequency estimator to the spurious tones is investigated and compared with those of different state-of-the-art frequency estimators through computer simulations.

FFT Applications: Tips and Tricks

Abstract: In this chapter some important FFT applications in DSP field are presented, mainly to spectral analysis. We learn how to exploit FFT for efficient and flexible calculations of the following DSP functions: discrete Fourier transform (DFT) and its zoomed as well as interpolated (IpDFT) version, discrete-time Fourier transform (DtFT), short-time Fourier transform function, signal correlation function and power spectral density (PSD), finally, signal convolution.

Improvement of signal processing in Coriolis mass flowmeters for gas-liquid two-phase flow

Abstract: As an increasingly popular flow metering technology, Coriolis mass flowmeter exhibits high measurement accuracy under single-phase flow condition and is widely used in the industry. However, under complex flow conditions, such as two-phase flow, the measurement accuracy is greatly decreased due to various factors including improper signal processing methods. In this study, three digital signal processing methods—the quadrature demodulation (QD) method, Hilbert method, and sliding discrete time Fourier transform method—are analyzed for their applications in processing sensor signals and providing measurement results under gas-liquid two-phase flow condition. Based on the analysis, specific improvements are applied to each method to deal with the signals under two-phase flow condition. For simulation, sensor signals under single- and two-phase flow conditions are established using a random walk model. The phase difference tracking performances of these three methods are evaluated in the simulation. Based on the digital signal processor, a converter program is implemented on its evaluation board. The converter program is tested under single- and two-phase flow conditions. The improved signal processing methods are evaluated in terms of the measurement accuracy and complexity. The QD algorithm has the best performance under the single-phase flow condition. Under the two-phase flow condition, the QD algorithm performs a little better in terms of the indication error and repeatability than the improved Hilbert algorithm at 160, 250, and 420 kg/h flow points, whereas the Hilbert algorithm outperforms the QD algorithm at the 600 kg/h flow point.

Discrete Fourier Transforms: DtFT and DFT

Abstract: In this chapter we investigate a big family of Fourier transforms: continuous Fourier transform (CFT), Fourier series (FS), discrete-time Fourier transform (DtFT), and discrete Fourier transform (DFT) The DFT, in its fast form (FFT), is probably one of the most frequently used orthogonal transforms in the world apart from the discrete cosine transform (DCT) We learn that DtFT originates from continuous Fourier transform, while DFT from Fourier series We become familiar with transform features and understand their strong and weak points We learn the fundamentals of frequency analysis of discrete-time signals by DtFT and DFT We see the significance of special signal shaping functions called windows in spectral analysis of signals