Synthesis of Low Peak-to-Peak Waveforms with Flat Spectra

Takafumi HAYASHI

Synthesis of Low Peak-to-Peak Waveforms with Flat Spectra

Takafumi HAYASHI

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This paper presents both new analytical and new numerical solutions to the problem of generating waveforms exhibiting a low peak-to-peak factor. One important application of these results is in the generation of pseudo-white noise signals that are commonly uses in multi-frequency measurements. These measurements often require maximum signal-to-noise ratio while maintaining the lowest peak-to-peak excursion. The new synthesis scheme introduced in this paper uses the Discrete Fourier Transform (DFT) to generate pseudo-white noise sequence that theoretically has a minimized peak-to-peak factor, F_p-p. Unlike theoretical works in the literature, the method presented here is based in purely discrete mathematics, and hence is directly applicable to the digital synthesis of signals. With this method the shape of the signal can be controlled with about N parameters given N harmonic components. A different permutation of the same set of offset phases of the "source harmonics" creates an entirely different sequence.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E81-A No.9 pp.1902-1908

Publication Date: 1998/09/25

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Category: Circuit Theory

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Takafumi HAYASHI, "Synthesis of Low Peak-to-Peak Waveforms with Flat Spectra" in IEICE TRANSACTIONS on Fundamentals, vol. E81-A, no. 9, pp. 1902-1908, September 1998, doi: .
Abstract: This paper presents both new analytical and new numerical solutions to the problem of generating waveforms exhibiting a low peak-to-peak factor. One important application of these results is in the generation of pseudo-white noise signals that are commonly uses in multi-frequency measurements. These measurements often require maximum signal-to-noise ratio while maintaining the lowest peak-to-peak excursion. The new synthesis scheme introduced in this paper uses the Discrete Fourier Transform (DFT) to generate pseudo-white noise sequence that theoretically has a minimized peak-to-peak factor, F_p-p. Unlike theoretical works in the literature, the method presented here is based in purely discrete mathematics, and hence is directly applicable to the digital synthesis of signals. With this method the shape of the signal can be controlled with about N parameters given N harmonic components. A different permutation of the same set of offset phases of the "source harmonics" creates an entirely different sequence.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e81-a_9_1902/_p

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@ARTICLE{e81-a_9_1902,
author={Takafumi HAYASHI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Synthesis of Low Peak-to-Peak Waveforms with Flat Spectra},
year={1998},
volume={E81-A},
number={9},
pages={1902-1908},
abstract={This paper presents both new analytical and new numerical solutions to the problem of generating waveforms exhibiting a low peak-to-peak factor. One important application of these results is in the generation of pseudo-white noise signals that are commonly uses in multi-frequency measurements. These measurements often require maximum signal-to-noise ratio while maintaining the lowest peak-to-peak excursion. The new synthesis scheme introduced in this paper uses the Discrete Fourier Transform (DFT) to generate pseudo-white noise sequence that theoretically has a minimized peak-to-peak factor, F_p-p. Unlike theoretical works in the literature, the method presented here is based in purely discrete mathematics, and hence is directly applicable to the digital synthesis of signals. With this method the shape of the signal can be controlled with about N parameters given N harmonic components. A different permutation of the same set of offset phases of the "source harmonics" creates an entirely different sequence.},
keywords={},
doi={},
ISSN={},
month={September},}

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TY - JOUR
TI - Synthesis of Low Peak-to-Peak Waveforms with Flat Spectra
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1902
EP - 1908
AU - Takafumi HAYASHI
PY - 1998
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E81-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 1998
AB - This paper presents both new analytical and new numerical solutions to the problem of generating waveforms exhibiting a low peak-to-peak factor. One important application of these results is in the generation of pseudo-white noise signals that are commonly uses in multi-frequency measurements. These measurements often require maximum signal-to-noise ratio while maintaining the lowest peak-to-peak excursion. The new synthesis scheme introduced in this paper uses the Discrete Fourier Transform (DFT) to generate pseudo-white noise sequence that theoretically has a minimized peak-to-peak factor, F_p-p. Unlike theoretical works in the literature, the method presented here is based in purely discrete mathematics, and hence is directly applicable to the digital synthesis of signals. With this method the shape of the signal can be controlled with about N parameters given N harmonic components. A different permutation of the same set of offset phases of the "source harmonics" creates an entirely different sequence.
ER -