In Multi-frequency Impedance Spectroscopy (EIS) systems, the nature and dynamic range of the imposed signal is very important. Using modern Digital Signal Processing (DSP) techniques, we can generate sophisticated signals which can be applied to a variety of systems under test. In this work, we present the development of a DSP-based instrument for the simultaneous real-time measurement of the impedance at many frequencies using an optimized imposed signal. For the implementation of this technique, an integrated environment using DSP hardware and software was developed. A gradient-descent type algorithm, rather than phase randomization, has been devised for the design of a multi-frequency signal which has adjusted phases for the individual frequency components to minimize the amplitude of the composite signal. This new imposed signal fully exploits the theoretical properties of the Discrete Fourier Transform (and Discrete Fourier Series), when applied to band-limited signals, improving the accuracy and extending the limits of the instrument.}
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