Sum of Sine Wave Excitation Signals

It seems that the best way to obtain a response to multiple frequencies is to apply a sum of odd harmonic sine waves, where / are /, 3f, 5f... (2n + 1)/, 

It can be seen from Fig. 3.10 that noise is always larger at low frequencies. This means that in order to obtain good data one should use larger amplitudes at low frequencies, while they could be lower at higher frequencies. Such a method was suggested by Popkirov and Schindler [105, 106]. They used the first impedance measurement as a test and adjusted amplitudes of all the sine waves, a, as proportional to the impedance modulus  

It is evident that amplitude optimization reduces noise significantly, by a factor of about 4-5. Garland et al. [107] proposed to decrease the amplitude by a factor of two per decade of frequencies. This avoids the necessity of repetition of measurements. The authors also proposed to use a chirp-z transform to carry out a discrete Fourier transform in the case where the number of points is V 2.  

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