Single Sine and FFT Measurement Techniques

The use of FFT (fast Fourier transform) spectral analysis can be the perfect complement to the single sine analysis technique. The FFT can perform very fast measurements since it is not necessary to sweep the stimulus frequency in order to measure multiple frequencies. With the introduction of DSP technology, very fast 

The choice of frequencies that are included in the multisine stimulus waveform is an interesting area for discussion. In the case where all frequencies are stimulated in the applied multisine waveform, the FFT analysis is not able to differentiate between signals that are the response of the cell to the same frequency in the stimulus waveform, or signals that are simply harmonics of the stimulus frequencies due to the nonlinearity of the cell, and this can lead to very poor results. Of course it is 

Much improved measurement can be obtained by reducing the number of stimulus frequencies in the multisine waveform. Some commercially available analyzers have either a preprogrammed list of frequencies or allow the multisine frequencies to be selected by the user. In this case, many frequencies in the FFT analysis band are deliberately not stimulated. The applied multisine frequencies are usually chosen so that each stimulus frequency is not coincident with the main harmonics of lower frequencies. In this case, the main components of harmonic distortion from each frequency in the stimulus waveform do not interfere with other stimulus frequencies (though of course it is not possible to avoid all significant harmonic frequencies). Without doubt, the impedance results from this approach are much improved compared to those obtained by the method where all frequencies are stimulated. 

Great care must also be exercised in the acquisition of data that is to be used for FFT analysis. In order to avoid problems with aliasing of frequencies (see section 3.1.3.4 for a discussion of this problem), it is essential to apply rigorous analog and digital filtering techniques, and the measurement sample rate must be sufficiently high (at least two times the maximum frequency of interest) otherwise out of band 

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