Error Analysis of Reconstruction From Linear Canonical Transform-Based Sampling

Shi, Jun; Li, Xiaoping; Yan, Feng-Gang; Song, Wei

doi:10.1109/tsp.2018.2793866

Cited by 31 publications

(16 citation statements)

References 43 publications

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“…

\int_{- \infty}^{+ \infty} {(1 + ω^{2})}^{r} {|φ (ω)|}^{2} italicdω < \infty

r = italicsup ({}, r : \int_{- \infty}^{+ \infty} {(1 + ω^{2})}^{r} {|φ (ω)|}^{2} italicdω < \infty) .

This is defined for the rank 2 wavelet. A wavelet with large regularity approaches an ideal filter, and therefore, the FB will have better performance .…”

Section: Proposed Waveletmentioning

confidence: 99%

A new discrete wavelet transform appropriate for hardware implementation

Meshkat

Dehghani

2020

Circuit Theory & Apps

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Summary A new method for computation of discrete wavelet transform is introduced. The impulse response of the finite impulse response (FIR) filter, as the main block in filter bank method, is realized such that orthonormal wavelet transform is achieved without using any multiplier as the most challenging part of the FIR filters. It is proved that the calculated Sobolev regularity of the proposed wavelet is higher than that of Daubechies for the same support width. Compared with most popular known wavelets, simulation results of the newly introduced wavelet for signal denoising prove remarkable advantage of our wavelet especially in terms of complexity and power consumption. The proposed wavelet and well‐known Daubechies wavelet are separately implemented on the Spartan‐6 FPGA (Field Programmable Gate Array) to compare the performance of them. The occupied slices and LUTs (Lookup Table) in realization of the proposed wavelet in comparison with those of Daubechies wavelet are decreased by 50% and 56%, respectively. Its power consumption at 100 MHz is also reduced by 86% in comparison with the Daubechies wavelet, and maximum frequency is increased by 186%. Implementation with standard cells of a 0.18‐μm CMOS (Complementary Metal Oxide Semiconductor Field Effect Transistor) technology shows 75% and 85% reduction in the power and chip area, respectively.

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“…

\int_{- \infty}^{+ \infty} {(1 + ω^{2})}^{r} {|φ (ω)|}^{2} italicdω < \infty

r = italicsup ({}, r : \int_{- \infty}^{+ \infty} {(1 + ω^{2})}^{r} {|φ (ω)|}^{2} italicdω < \infty) .

This is defined for the rank 2 wavelet. A wavelet with large regularity approaches an ideal filter, and therefore, the FB will have better performance .…”

Section: Proposed Waveletmentioning

confidence: 99%

A new discrete wavelet transform appropriate for hardware implementation

Meshkat

Dehghani

2020

Circuit Theory & Apps

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“…The linear canonical transform (LCT) with real parameter matrix A of signal f (t) is defined as [16][17][18]…”

Section: Simplified Linear Canonical Transformmentioning

confidence: 99%

“…The linear canonical transform (LCT) with real parameter matrix

A

of signal

f false(t false)

is defined as [16–18]

L_{f}^{bold-italicA} false(u false) = \int_{R} f false(t false) K_{bold-italicA} false(t, u false) d t

with the kernel

K_{bold-italicA} false(t, u false) = ({, \begin{matrix} 1em4pt \\ \frac{1}{\sqrt{i b}} e^{normali π ((a t^{2} + d u^{2} - 2 t u) / b)} & b \neq 0 \\ \sqrt{d} e^{i false(c d u^{2} / 2 false)} δ false(t - d u false) & b = 0 \end{matrix})

where the real parameter matrix

A = ()(, \begin{matrix} 1em4pt \\ a & b \\ c & d \end{matrix})

satisfying

a d - b c = 1

and

L_{f}^{bold-italicA} false(u false)

denotes the LCT of

f false(t false)

.…”

Section: Simplified Linear Canonical Transformmentioning

confidence: 99%

Method for parameter estimation of LFM signal and its application

Guo

Yang

2019

IET signal process.

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A linear frequency modulation (LFM) signal is a typical non-stationary signal, and its parameter estimation has always been among the core issues in the field of signal processing. In this study, a novel method for parameter estimation of LFM signal is proposed using the simplified linear canonical transform and evaporation-rate-based water cycle algorithm. According to the results obtained from the theoretical analysis and experimental simulation, the proposed method possesses the advantages of easy implementation, high precision and independence on initial values compared with the concise fractional Fourier transform (CFRFT)-based and fractional Fourier transform-based methods. Moreover, the proposed parameter estimation method is successfully applied to optical measurement with improving measurement accuracy.

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“…Huo and Sun 19 demonstrated aliasing error and truncation error estimations for LCT sampling series with respect to random signals. Shi et al 20 derived a closed‐form expression for the integrated squared error in the LCT domain. Annaby and Asharabi 21 introduced derivative sampling theorem in the LCT domain and gave rigorous error estimates for truncation error, amplitude error, and jitter‐time error for LCT derivative sampling series, respectively.…”

Section: Introductionmentioning

confidence: 99%

Truncation error estimates for two‐dimensional sampling series associated with the linear canonical transform

Huo

2021

Math Methods in App Sciences

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The linear canonical transform (LCT) provides a more general framework for many well‐known linear integral transforms, such as Fourier transform, fractional Fourier transform, Fresnel transform, and so forth, in digital signal processing and optics. There has been a great deal of research on sampling expansions of bandlimited signals in the LCT domain. However, results on error estimation and convergence analysis appear to be relatively rare, especially for multi‐dimensional sampling series associated with the LCT. In this paper, we present error estimation and convergence analysis for two‐dimensional (2D) sampling series in the LCT domain. Specifically, we first prove the absolute convergence and uniform convergence of 2D LCT sampling series. Then, we analyze truncation error estimates for uniformly sampling 2D bandlimited signals in the LCT domain, as well as deriving three truncation error bounds. Finally, our theoretical results are demonstrated by numerical examples.

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Error Analysis of Reconstruction From Linear Canonical Transform-Based Sampling

Cited by 31 publications

References 43 publications

A new discrete wavelet transform appropriate for hardware implementation

A new discrete wavelet transform appropriate for hardware implementation

Method for parameter estimation of LFM signal and its application

Truncation error estimates for two‐dimensional sampling series associated with the linear canonical transform

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