A Calibration Method of Short‐Time Waveform Signals Passed Through Linear Time‐Invariant Systems: 1. Methodology and Simple Examples

Abstract

AbstractWe propose an 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 deconvolution in the time domain, and there is an equivalent operation in the frequency domain with the Fourier transform. For the short‐time data, 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 method to eliminate the modification of the multiplied window function. In the 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 should be useful for the calibration of general radio wave signals passed through LTI systems as well as for the calibration of plasma waves observed in space.