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\begin{document}

\title{A Novel Calibration Method of Short-Time Waveform Signals Passed through
LTI Systems: 1. Methodology and Simple Examples}



\author[1]{Masahiro Kitahara}%
\author[2]{Shoya Matsuda}%
\author[3]{Yuto Katoh}%
\author[4]{Hirotsugu Kojima}%
\author[2]{Yoshiya Kasahara}%
\author[5]{Yoshizumi Miyoshi}%
\author[1]{Satoko Nakamura}%
\author[6]{Mitsuru Hikishima}%
\affil[1]{Nagoya University}%
\affil[2]{Kanazawa University}%
\affil[3]{Tohoku University}%
\affil[4]{Kyoto University}%
\affil[5]{Institute for Space-Earth Environmental Research, Nagoya University}%
\affil[6]{Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency}%


\vspace{-1em}



  
  \date{June 13, 2024}


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\begin{abstract}
We propose a novel and accurate calibration method for short-time
waveform signals passed through a linear time-invariant (LTI) system
that has a non-negligible group delay. Typically, the calibration
process of waveform data is expressed by the Fourier transform and is
performed in the frequency domain. If the short-time Fourier transform
is applied to the waveform data in the calibration process, multiplying
the data by a window function is highly recommended to reduce side-lobe
effects. However, the multiplied window function is also modified in the
calibration process. We analyzed the modification mathematically and
derived a novel method to eliminate the modification of the multiplied
window function. In the novel method, calibrated data in the frequency
domain are inverse-transformed into waveform data at each frequency,
divided by a modified window function at each frequency, and accumulated
over the frequencies. The principle of this method derived
quantitatively indicates that the calibration accuracy depends on the
transfer function of the system, frequency resolution of the Fourier
transform, type of the window function, and typical frequency of the
waveform data. Compared with conventional calibration methods, the
proposed method provides more accurate results in various cases. This
method is useful for calibration of general radio wave signals through
passed LTI systems as well as for calibration of plasma waves observed
in space.%
\end{abstract}%



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