Mathematical analysis of blackman window function in fractional Fourier transform domain

Agarwal, Prabhakar; Singh, Shashi Kant; Pandey, Vishal

doi:10.1109/medcom.2014.7005988

Cited by 2 publications

(2 citation statements)

References 11 publications

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“…In linear spectrum analysis, the amplitude coefficient is generally used as the correction factor. The energy coefficient is generally used in the power spectrum [31,32]. In this paper, eight window functions (apodization functions), including Boxcar, Triangular, Happ-Genzel, Blackman-Harris 3 terms, Blackman-Harris 4 terms, Norton-Beer Weak, Norton-Beer Medium and Norton-Beer Strong, were used to process the THz spectra.…”

Section: Data Processingmentioning

confidence: 99%

Molecular Characterization and Theoretical Calculation of Plant Growth Regulators Based on Terahertz Time-Domain Spectroscopy

Lin

Cai

et al. 2018

Applied Sciences

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Terahertz (THz), as an advanced spectral technology, has unique absorption characteristics for most biological macromolecules. In this work, the theoretical fundamentals for the application of THz time-domain spectroscopy (THz-TDS) to molecular characterization and fingerprint peak detection of three plant growth regulators (PGRs), including 2,4-Dichlorophenoxyacetic acid (2,4-D), forchlorfenuron (CPPU) and indole-3-acetic acid (IAA) were researched. Meanwhile, the effects of eight types of window functions on THz spectra were studied when converting time-domain spectra into frequency-domain spectra by Fourier transform. Based on the optimal window function, the THz absorption coefficient and refractive index of PGRs in frequencies of 0.2-3 THz were extracted. The molecule structure and vibration mode of three PGR samples were simulated by using density functional theory (DFT). The results showed that the three PGRs had different fingerprint peaks. Characteristic absorption and anomalous dispersion of 2,4-D were found at 1.35, 1.57 and 2.67 THz, those of CPPU were found at 1.77 and 2.44 THz, and the absorption peak of IAA was located at 2.5 THz. The absorption peaks obtained from THz spectra were identified according to the theoretical calculation results of DFT. These fingerprint peaks in THz spectra were generated by the interior stretching vibration and external deformation vibration of molecular groups. The experimental results revealed the feasibility of identifying PGRs species and detecting residues using THz-TDS.

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Section: Data Processingmentioning

confidence: 99%

Molecular Characterization and Theoretical Calculation of Plant Growth Regulators Based on Terahertz Time-Domain Spectroscopy

Lin

Cai

et al. 2018

Applied Sciences

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“…To make use of the excellent properties of Shannon wavelet, researchers proposed many methods to improve it. The methods are usually used to improve the compact support by introducing windows functions [42,43], such as Meyer window [44], Nuttall window, Blackman window [45], Gauss window [46,47], etc. Similar to windowed Fourier transform, windowing function accelerates the delay speed of Shannon wavelet function, but it also destroys the normalization characteristic of Shannon function.…”

Section: Shannon-cosine Interpolation Waveletmentioning

confidence: 99%

Hermite Interpolation Based Interval Shannon-Cosine Wavelet and Its Application in Sparse Representation of Curve

Wang

Mei

et al. 2020

Mathematics

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Using the wavelet transform defined in the infinite domain to process the signal defined in finite interval, the wavelet transform coefficients at the boundary are usually very large. It will bring severe boundary effect, which reduces the calculation accuracy. The construction of interval wavelet is the most common method to reduce the boundary effect. By studying the properties of Shannon-Cosine interpolation wavelet, an improved version of the wavelet function is proposed, and the corresponding interval interpolation wavelet based on Hermite interpolation extension and variational principle is designed, which possesses almost all of the excellent properties such as interpolation, smoothness, compact support and normalization. Then, the multi-scale interpolation operator is constructed, which can be applied to select the sparse feature points and reconstruct signal based on these sparse points adaptively. To validate the effectiveness of the proposed method, we compare the proposed method with Shannon-Cosine interpolation wavelet method, Akima method, Bezier method and cubic spline method by taking infinitesimal derivable function cos(x) and irregular piecewise function as an example. In the reconstruction of cos(x) and piecewise function, the proposed method reduces the boundary effect at the endpoints. When the interpolation points are the same, the maximum error, average absolute error, mean square error and running time are 1.20 × 10−4, 2.52 × 10−3, 2.76 × 10−5, 1.68 × 10−2 and 4.02 × 10−3, 4.94 × 10−4, 1.11 × 10−3, 9.27 × 10−3, respectively. The four indicators mentioned above are all lower than the other three methods. When reconstructing an infinitely derivable function, the curve reconstructed by our method is smoother, and it satisfies C2 and G2 continuity. Therefore, the proposed method can better realize the reconstruction of smooth curves, improve the reconstruction efficiency and provide new ideas to the curve reconstruction method.

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Mathematical analysis of blackman window function in fractional Fourier transform domain

Cited by 2 publications

References 11 publications

Molecular Characterization and Theoretical Calculation of Plant Growth Regulators Based on Terahertz Time-Domain Spectroscopy

Molecular Characterization and Theoretical Calculation of Plant Growth Regulators Based on Terahertz Time-Domain Spectroscopy

Hermite Interpolation Based Interval Shannon-Cosine Wavelet and Its Application in Sparse Representation of Curve

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