Multisine signal with a low crest factor (CF) can bring a high signal-to-noise ratio for fast frequency response function (FRF) estimation. Synthesis of a low CF multisine with the given amplitude spectrum depends on optimum selection of the initial phases of its cosinusoidal components. The solutions investigated can be generally divided into two branches: (1) the analytical method based on direct formula calculation; and (2) the numerical method based on iterative computations. The analytical method works well only for an equidistant and flat amplitude spectrum, while the numerical method can generally output better results, even for a sparse or non-flat spectrum, but the number of iterations might be huge. This paper presents an improved CF minimization algorithm to synthesize multisine signals based on the combination of the previous Schroeder analytical method and the Van der Ouderaa (VDO) iteration procedure. The improved algorithm adopts the Schroder phases as the iterative initial phases, and employs a logarithmic clip function of the iterative index i in the VDO iteration procedure. Comprehensive experiments of multisine synthesis on three types of cosinusoidal amplitude spectra are performed, and the resulting CFs remain the lowest level in all cases compared with the earlier methods. The proposed algorithm provides a fast and efficient solution to synthesize multisine with the lowest CF for an arbitrary user-prescribed spectrum.

Bioimpedance spectroscopy (BIS) measurement methods have been evolving from the traditional frequency-sweep approach to the multi-frequency simultaneous measurement technique which can drastically reduce measuring time and will be increasingly attractive for time-varying biological applications. Multi-frequency mixed (MFM) signals with sparsely distributed spectra are desirable for broadband BIS measurement. This paper proposes a synthesis method to design a series of tri-level MFM signals which contain only three values (+1, 0, -1), and has majority energy distributed on its (2(n))th primary harmonics. Tri-level MFM signals have both high energy efficiency and a low crest factor. An impedance measurement experiment excited by an 8th-order tri-level MFM signal on a RC three-element equivalent model has been performed, and the results on 8 primary harmonic frequencies ranging from 8 to 1024 kHz show a high accuracy with the mean amplitude relative error of 0.41% and mean phase absolute error of 0.18°, which has validated the feasibility of the tri-level MFM signals for broadband BIS measurement.

Wideband current sources that can work stable over a wide frequency range with large load variations are critical for the performance of electrical impedance spectrum (EIS) measurements. In this paper, we design a wideband mirrored current source (MCS) using two simple differential difference amplifiers (DDA) AD830. PSpice simulation and measurement were performed on load resistances from 100 Ω to 1500 Ω over the frequencies up to 1 MHz. The maximum variation of the output current is less than 0.5% over the whole bandwidth and the output impedance is 4.2 MΩ at 100 Hz and greater than 185 kΩ at 1 MHz. Moreover, less than 1% linearity error (the V IN versus the I OUT ) of the output current I OUT from 1 mA to 20 mA was achieved by sweeping the input voltage signal V IN from 0.1 V to 2 V at 100 Hz, 1 kHz and 10 kHz respectively. The DDA-based wideband MCS has high accuracy, linearity and simple structure, which may improve the performance of EIS measurements and other relevant applications.

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