## 3 IBC Time Domain Responses Based on Corrected Transfer Function  
Due to the frequency dependence of the transfer function (7), a transmitted signal would suffer dispersion and amplitude reduction. In digital communication, this phenomenon will cause pulse spreading and overlapping in the transmitted pulses. Hence, this will hinder the data communication rate. For this reason, both baseband and passband transmissions have been investigated by transmitting square waves into the IBC channel to assess the channel dispersion and distortion behavior parameters, which could assist in IBC design. In this Section, we study the IBC time domain channel characteristics with the corrected analytical model discussed in Section 2.2. For simplicity, only Subject B calculation and measurement results are shown throughout this Section. For baseband experiments, the general measurement set-up block diagram displayed in Figure 5(a) was used. It consists of a function generator (Agilent, 33250A Function/Arbitrary waveform generator),  
Figure 4: Measured and calculated (with correction) transfer function characteristic of (**a**) subject A; (**b**) subject B.  
a differential probe and an oscilloscope (Agilent, MSO6104A Mixed signal oscilloscope). As usual, all experiments done here have been performed carefully to take care of the common ground problem by using a differential probe (Agilent, 1141A) and battery-powered equipment. The flow chart is shown in Figure 5(b). During the experiment, the 500 Hz square wave with 50% duty-cycle (1 ms pulse width), peak-to-peak amplitude of 1 V from the function generator was applied to the cleansed human limb directly, and the received signals were detected via differential probe. The time domain signals were showed in the oscilloscope for recording. On the calculation side, given the transfer function, the calculated output signal in time-domain can be obtained by taking the Inverse Fourier Transform (IFT) of the product of the transfer function and the Fourier Transform (FT) of the input signal. The corresponding output results for input square waves in baseband transmission in calculations and experiments are displayed in Figure 6. As shown in Figure 6(a,b), the calculated results are consistent with the measured results. Less attenuation transmissions occur near the time instants around 0 and 1 ms while large attenuation/distortion happens elsewhere. These spike-like outputs for pulse-input phenomena demonstrate that galvanic-type IBC channel for baseband transmission is very dispersive. The reason is that pulse amplitude changes in input lead to high frequency components, and high frequency components pass easier than lower frequency components as discussed in our previous Section. These non-flat frequency responses belong to a form of distortion that occurs when different  
Figure 5: IBC channel baseband and passband transmission experiment set-ups: (**a**) General block diagram; (**b**) Flow chart for baseband transmission experiment; and (**c**) Flow chart for passband transmission experiment. frequencies are attenuated by different amounts, resulting to severe distortion for pulse transmissions. In order to quantify the output waveform distortion for the baseband input, the total harmonic distortion among the first four non-zero harmonics: (_THD\({}_{4}\)_) is defined as:  
\[\textit{THD}_{4}=\frac{\sqrt[4]{\frac{4}{2}\textit{non - zero harmonic powers}}}{\textit{fundamental harmonic voltage}} \tag{11}\]  
The reason why we take only up to the 4 th harmonics here is to have a fair comparison with passband transmission which will be discussed later in this Section. Like the 500 Hz square wave transmitted in the baseband channel, low frequency harmonics suffer higher attenuation, which will cause _THD\({}_{4}\)_ higher than that of ideal square wave around 41.4%. The calculation square wave _THD\({}_{4}\)_ result is around 96% while the corresponding measurement _THD\({}_{4}\)_ results are 99.7% and 99.2% for S = 6 cm and 11 cm, respectively.