Wideband Signal Generation Using Egyptian Fractions and Application to Instantaneous Impedance Measurements

Abstract

In this work, we investigate the use of Egyptian fractions to construct wideband signals with a near-flat power spectrum. In particular, it is well-known that wideband signals can be obtained using composite multisine signals. However, the choice of the frequencies and/or phase shifts in these sinusoids is critical to approach a flat power spectrum with a low crest factor. A number of known methods, such as using Rudin-Shapiro polynomials or random phases, have been used in this problem. However, the use of Egyptian fractions has not been explored yet, despite being easier to generate and implement. Here, we construct multisine signals (in the form of a voltage) based on different Egyptian fraction sequences (EFSs) and use them to measure the linear time-invariant impedance of an RC circuit and then the instantaneous impedance of nonlinear time-varying solar cell. Two methods are used to generate these signals: 1) the EFSs are assigned to the phase angles or 2) they are used to set the values of the angular frequencies. The accuracy of measurements is assessed via comparison to the standard sine-sweep method using a research-grade Biologic VSP-300 electrochemical station showing acceptable results.