The calculated SNR at the modulator and decimation filter output, as shown in Figure 3.11, demonstrated that the proposed design with or without compensation successfully
filters the out-of-band quantization noise while preserving the SNR in the signal band without detrimental group delay distortion. In Figure 3.12 it is shown that the use of phase compensation filters reduces the group delay variations in the frequency band of
ν 00.125 which directly effects the amount of time delay each frequency component
is exposed to. Furthermore, in Table 3.1 the amount of the group delay variations in the
frequency bands of ν 0 0.0625 and ν 0 0.125 are presented in terms of samples
and µsec as the proposed filters are designed as discrete time digital filters. These sample values can be easily converted into seconds by simply dividing them into the
oversampling frequencies which are indicated as fs1 46.08kHz and fs2 64kHz for
MIT-BIH Arrhythmia Database and TWAC Database, respectively. In order to provide a more detailed understating of Table 3.1, lets look at the fourth and sixth columns which present the amount of group delay variation for decimation filters without and with phase compensation in the bands of interest, in terms of µsec. In the band of
ν 00.0625 the group delay variation for the proposed decimation chain is measured
as 29 µsec which indicates that if a frequency component at DC (ν 0) is delayed
by 0 second, the frequency component at ν 0.0625 will be delayed by 29 µsec. On
the other hand, use of phase compensation filters reduces this variation to 3.44 µsec. This will effectively lead to a misalignment of the time domain signal which will result in signal distortion and thus, lower group delay variation indicates less distortion. Although phase compensation reduces the group delay variation, the values obtained without phase compensation are comparatively low regarding to the wave durations and normal limits of a standard ECG features as presented in Table 2.1. This provides a good indication that the phase compensation is not compulsory for this application,
nevertheless further simulations are carried out in order to evaluate the effect of phase
non-linearity on different ECG data records. The results of these simulations are
presented in Figures 3.15 and 3.18 which show the waveform dissimilarity and distortion ratio for each ECG data record of the two aforementioned databases. In both figures, the blue and red bars present the results of analysis obtained without and with phase compensation, respectively. In Figure 3.15 (a) the waveform dissimilarity for six TWAC ECG data records are presented and it can be observed that the utilization of phase compensation filters reduces the amount of waveform dissimilarity. Amongst these six data records, twa90 shows higher values which is related to the power of the signal. twa90 record is observed to have lower signal power, calculated as the average sum of the absolute squares of the time-domain samples, when compared to the other data sets which shows that the signal of interest is more effected by the high frequency noise.
As the group delay variation increases at higher frequencies than ν 0.125 this leads
to increased signal distortion and thus increased waveform dissimilarity. However, the values presented in this figure are in the order of 104 which is a negligible mismatch. In addition, Figure 3.15 (b) presents the distortion ratio where phase compensation reduces the distortion ratio, as expected. The twa46 and twa90 records present higher ratios as opposed to the other signals which is due to having lower signal power. As DR is a ratio of the power of difference between the magnitude of the original data and the decimation filtered data, to the power of the signal, the DR values can vary for different signals. The DR results are also dependent on the frequency content of the signals. When the signal has more high frequency components the signal faces more distortion due to the increasing group delay variation which affects the effectiveness of the phase
compensators as can be seen from the difference between the red bars for these two data records. Although, phase compensation filters reduce DR and waveform dissimilarity, the results obtained without phase compensation is negligible. Therefore, it is not crucial to use phase compensation filters which will increase the hardware and algorithm complexity. Furthermore, Figures 3.18 (a) and (b) present the waveform dissimilarity and DR for the ECG data records obtained from the MIT-BIH Arrhythmia Database. Similarly, phase compensation filters reduces the signal distortion for all data records.
The two conditions, Ventricular bigeminy (B) and 2 heart block (BII) presented in
both figures exhibits relatively higher waveform dissimilarity and DR, compared to the other cardiac conditions. Power of these signals are calculated to be lower than the rest of the signals which leads to a relatively higher distortion ratio and waveform, since according to (3.11) decreasing signal power, increases the distortion ratio and waveform dissimilarity.
The simulation results obtained by using two ECG data sets with different diagnostic importance, the spectral similarity for both sets of data (healthy and unhealthy) is determined to be approximately the same due to the passband characteristics of the decimation filters. Morphological similarity between the filter input and the output is too high for the filters without compensation in the case of both normal sinus rhythm and arrhythmia. In addition, since the mean amplitude error is negligibly small and almost the same for both filters, the use of the compensation filter is not necessary, thus saving power and cost by avoiding the use of extra hardware. This is due to the fact that more than 99 % of the signal energy is concentrated in the frequency range
results are obtained for each data set, it should be noted that, biopotential signals are non-stationary and there is no standard one best solution for them. Overall results have proven that proposed design do not cause any drastic distortion which might lead to misdiagnosis.
The comparisons with the state-of-the art filters and the filters implemented accord- ing to the state-of-the-art algorithms, presented in Table 3.2, demonstrated that the proposed polyphase structures are superior to others since they provide very small passband ripples (0.47µdB) and sufficient stopband attenuation with negligible group delay variation in the band of interest. The proposed design requires no multiplier which makes it superior to the filter designed by [120], whilst they exhibit almost the same magnitude characteristics. Although, [121] is a multiplier free design as well, it requires almost twice the number of adders in order to achieve a stopband attenuation of -80 dB and suffers from having large passband ripples. In addition, the group delay variation introduced by the proposed design is almost half of the group delay variation introduced by [120] and [121]. Cascading two polyphase structure provides a very high stopband attenuation and micro dB passband ripples. However, the performance of a single polyphase filter incorporated in a decimation chain is sufficient enough to at- tenuate the out-of-band quantization noise and prevent aliasing, therefore there is no need for using higher order filters with increased group delay variation.