VOLUME: 08, Special Issue 09, (TTME-2021) Paper id-IJIERM-VIII-IX, October 2021 9
STABLITY AND IMPULSE RESPONSE ANALYSIS OF OPTIMUM IIR FILTER FOR EEGARTIFACT REMOVAL
Nitn Jain
Dr. C.V. Raman University, Bilaspur India Dr. Shanti Rathore
Dr. C.V. Raman University, Bilaspur India
Abstract- Artifact removal methods are frequently being used for removing unwanted motion effects from the EEG signals. There are many filter design methodologies proposed in past for EEG filtering. The major advantage of such filter designing is to reduction in computing delay and falter order. There are many methods of designing the IIR filters. In this paper prime goal is to evaluate the designed response spectrums of the different proposed IIR filter methods for EEG artifact removal designs. An IIR filter using combination of pass-stop band filter and the optimum reduced order filter is compared and the stability is tested for transfer functions. Filters are designed for removing EEG signals motion artifacts. The Sept, Impulse and pole zero response are compared for testing the stability of filters.
Keywords- EEG, IIR Filters, Stability, Step Pole Zero Analysis,Reduced order IIR filter, MInMAX optimization
1.INTRODUCTION
The EEG signal are type of biological signals used for analyzing and observing the human brain activities for medical disease identification, but these signals suffers from motion artifacts added during the capturing times. Notch filters [1], Infinite Impulse Response (IIR) filters [2, 3, 4, and 5], FIR filter [8] were designed in past for removing these motion artifacts from EEG signals. In this paper major focus is to evaluate performance of filters based on analysis oftransfer functions stability and poles –zero plots. The artifacts EEG considered for the study are shown in the Figure 1.
Figure 1 EEG signals with artifacts for study
The orange highlighted section in Figure 1 represents the muscular motion artifacts also called (EMG) and the yellow section represents the eye blinks motions abbreviated as EOG artifacts. The EEG data base of the MIT-Scalp available at the physionet is used for testing the filter performance. Three channels as Ch-4, Ch-9 and Ch-13 are consider for evaluation asshown in Figure 1.
In this study the performance of the notch filter for the 8thorder design with cutoff frequency Wn=0.2 and pass band ripples of 1.5 decibels is tested. The performance is compared with our proposed filter design architecture with the IIR filter of 16th order. Paper proposed to design optimum reduced order IIR filter by optimizing the IIR filter transfer functions and there numerator/denominators coefficients. The proposed IR filter is a two stage pass-stop band filter. Frequency response comparisons of the designed notch filter and an IIR fitter is given in the Figure 2.
VOLUME: 08, Special Issue 09, (TTME-2021) Paper id-IJIERM-VIII-IX, October 2021 10
Figure 2 Comparison of Frequency Responses of a) Notch Filter and b) a proposed two Pass IIR Filters
The general form of the filter transfer function is defined as the ratio as;
𝑌 𝑠 =𝐵(𝑠)
𝐴(𝑠)∗ 𝑋 𝑠 (1)
The form of the IIR filter is in terms of the nth order coefficients of numerator and denominator are
𝐻 𝑠 =𝐻𝑁 𝑠
𝐻𝐷 𝑠 = 𝑏0+ 𝑏1∗ 𝑠 − − ∓ 𝑏𝑛−1𝑠𝑛 1 − 𝑎1∗ 𝑠 − − − ∓𝑎𝑛−1𝑠𝑛 2
In this paper the IIR filter is designed by combining the pass band and stop band Butterworth filters with transfer function defined as
hIIR= hBP∗ hSB (3)
Where,hBP is transfer function of the second order band pass filter and hSB, is the transfer function of 8th order stop band filter. The response of IIR filter is shown in the Figure 2 b).
2.EVALUATIONPARAMETEROFDIGITALFILTERS
There is various transfer function analysis methods used for evaluating performance of filter design. The parameter for evaluation flow for digital filter analysis is given in the Figure 3.The Filters are evaluated based on the stability, filters responses as step and impulse responses
Figure 3 Classification Filterdesign parameters for evaluations 3.LITERATUREREVIEW
There has been lot of digital filters designed to remove theexternal and internal noise.
Section reviewswork done for designing ofIIR filter for context of EEG signal smoothening [1]. In addition step and impulse response based works are also discussed.D. Pancholiet al [2] have studied EEG artifact removal methods for Brain Computer Interface (BCI). They have proposed various wavelet based CCA method for artifact removals. Shapna et al [3]
have designed IIR filters for denoising application and analyzed phase, and amplitude responses, group and phase delay to access performance but for higher order filters.
NaliniSet al [4] have compared Butterworth and Chebychef based IIR filters designs. V.
Lesnikov et al [5]have used the convergence of pole and zeros for numeric evaluation of IIR filter performance. They have used maximum number of zeroes in the transfer functions R.
Filter Analysis Methods
Stability Analysis
Filter Response
Impulse Response Frequency spectra Step Response
Pole-Zero Analysis
VOLUME: 08, Special Issue 09, (TTME-2021) Paper id-IJIERM-VIII-IX, October 2021 11
Punchalardet al [6] has presented the analysis of notch filter design for 50 Hz noise.Usually notch filter is used for removal of the power line interference.
Roy V, et al [7] has presented effective Method of GE-CCAusing the concept of Gaussian elimination in the wavelet domain. On the basis of frequency stability usually FIR filtersare more stable them the IIR falters. It is due to the limited numbers of zeroes in the FIR filter designs. Therefore it is challengingproblem to address stability issuesof the IIR filter design
M. Abu Naser et al [11] have presented various fundamental problems related to stability analysis of the IIR based filters. They used averaging theorem for stability analysis.H. Ko et al [12] have proposed a design of IIR filter which is a computationally efficient and robust too. They have performed analysis of the stability of the finite precision synthesis of the IIR filter. Jyoti Singhai et al [14] has used IIR filter for video stabilization of the hand held mobile videos.
TABLE 2 The summary of the review work on Filter designing’s
Authors Filter Algorithm Description Parameters
D. Pancholi et
al [2] Wavelet filter based on CCA
Have studied the EEG artifact removal for application in the robotics for automatic control methods using Brain Computer Interface (BCI).
SNR and MSE, Deviation.
Shapna et al
[3] IIR Filter Designed IIR filters for de noising application and analyzed parametric performance.
Phase, responses, group and phase delay.
NaliniS et al [4]
Butterworth &
Che by chef filters
Performance comparison of various filtersfordifferenthigher order of IIR filters.
Order and frequency response of filters.
Roy V, et al [7] Wavelet Filtered EEG artifact removal
Has presented effective GE-CCA using the concept of Gaussian elimination in the wavelet domain.
SNR, Deviation and ROC curves
M. Abu Naser
et al [11] Adaptive IIR Filter Have presented various fundamental problems related to stability analysis of the IIR based filters.
Stability analysis using pole and zeroes responce.
H. Ko et al
[12] IIR Filter design Have proposed a design of IIR filter which is a computationally efficient and robust too.
Stability Analysis
N. Ramesh et
al [13] Frictional band pass filter
Stability analysis for the designing of
the band pass filter Filter order, stability Proposed Reduced order
optimum IIR Filter based on the pass and stop band
Min-Max optimization based lower order IIR filter designing and response and stability analysis of the transfer functions for EEG artifact removal,
Step, impulse response, stability analysis
4. PROPOSED IIR FILTER DESIGN
This section of the paper presets the design steps and basic sequential transfer functions designs for stages as shown in the Figure 4. The goal of the any filter is to pass the desired low frequency band and stop higher frequency bands. This process is clear from flow chart of design.
4.1. Steps of Proposed IIR Filter Designing
The sequential steps for proposed IIR filter designing are presented in the Figure 6.
VOLUME: 08, Special Issue 09, (TTME-2021) Paper id-IJIERM-VIII-IX, October 2021 12 Figure 4 Design Flow of Filter Evaluation 4.2. Notch Filter Step response
Notch filter is used for filtering at 50 Hz. Along with pass band filter for EEG signals. The transfer function of the designed notch filter in this paper is shown as hnotch, for 8th order filter.
hnotch =
6.074e − 06s7+ 4.252e − 0 s6+ 0.0001275 s5 + 0.0002126 s4+ 0.0002126 s3+ 0.0001275 s2
+4.252e − 05s + 6.074e − 06 s7− 5.851s6± 15.26 s5− 22.93s4+ 21.41s3
− 12.4s2 + 4.125 s − 0.6086
(3)
The step response for Notch filter is shown in Figure 5. It looks flat and very close response to IIR response.
Figure 5.Step Response for Propose Transfer Function of Notch Filter
The thrasher functions derived for the second order Butterworth filter based pass band (BP) filter is given mathematically as;
𝐻𝐵𝑃 𝑠 = 0.2066 𝑠4− 0.4131 𝑠2+ 0.2066
𝑠4+ 0.5488 𝑠3+ 0.4535 𝑠2+ 0.1763s + 0.1958 (4)
Figure 6 Step Response of Band Pass Filter Stage
0 5 10 15 20 25
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3
n (samples)
Amplitude
Band Pass filter Step Responce
Initialize filter parameters Load EEG data
Declaration and Design Notch filter Design two stage IIR filter Optimize and reduced order Filter
design
Plot Impulse and step response
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The IIR filter is designed as combination of pass band and stop band filters. The transfer function for an EEG artifact removal based methods is given as the;
𝐻𝐼𝐼𝑅=
0.06531s16+ 0.8693s15+ 5.585s14+ 22.93s13 +67.23 s12+ 149.1 s11+ 258.5 s10+ 357.2 s9+ 397.4 s8+ 357.2 s7+ 258.5 s6+ 149.1 s5+ 67.23 s4
+22.93 s3+ 5.585 s2+ 0.8693s + 0.06531 s16+ 9.039 s15+ 39.16 s14+ 108.5 s13+ 215.7 s12+ 327.2 s11+ 392.2 s10+ 378.7 s9+ 297.8 s8+ 191.2 s7+ 99.83 s6+ 41.96 s5+ 13.91 s4
+ 3.518 s3+ 0.6403 s2+ 0.075 s + 0.004266 (4)
Figure 7 Step Response of IIR Filter Stage for EEG Channel
The optimum IIR filter is designed using the MIN-MAX optimization is applied over coefficients of the eq (5) to generate the reduced order IIR filter as the transfer function of second order filter.
𝐻𝑜𝑝𝑡 𝑠 = s2+ 4 s + 15
43 (5)
Figure 8 Step Response of the Proposed Optimum Reduced Order Filter Design 5. SATBLITY AND RESPONSE ANALYSIS
This section evaluated the stability criterion for different designed filters transfer functions.
The poles and zeroes are plotted for evaluating the stability of the designed filter responses.
Based on design results of the EEG signal filtering using the optimum reduced order IIR filter is shown in the Figure 9. The filtered signal follows the true nature of original EEG signalsas clear from the Figure 9. Figure presets the results for Ch-13 of the MIT scalp data base of 24 channel EEGs. The EOG eye blink is removed significantly by proposed method.
0 50 100 150 200 250
0 0.2 0.4 0.6 0.8 1 1.2 1.4
n (samples)
Amplitude
IIR filter Step Responce
0 0.5 1 1.5 2 2.5 3
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
n (samples)
Amplitude
Optimized Step responce
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Figure 9 Original EEG Ch-13 and reduced order optimally filtered artifact removed signal for proposed simulation.
5.1. Stability Analysis
In order to analyze the stability performance of the designed transfer functions of Notch filter, IIR filter and proposed optimum reduce order IIR filter the pole –zero analysis is done.Figure 10 presets results filtered signals and the respective pole zero plots. The results are shown for the EEG channel CH-9 having the muscular and the eye blink artifacts. The synthetic random noise is aided with EEG data and then results in each row are corresponds to the Notch filter, IIR filter and the Reduce order filter respectively. The stability of the filter depends on the position of the poles and the zeros of the transfer functions the z plane with respect to unit circle. For the filter to be stable poles must be in the left hand side of z plane
Figure 10 the stability analysis using the pole zero plots for three different filtezr designs
Table 2 Results of the Stability Performance of the Filter with their orders Parameter Notch Filter IIR Filter Optimum Reduce order filter
Filter order 8th 16th 2nd
Stability Less stable Stable closely Stable
0 500 1000 1500 2000 2500 3000
-1000 -500 0 500 1000 1500
Input EEG
Optimum IIR Filltered EEG
VOLUME: 08, Special Issue 09, (TTME-2021) Paper id-IJIERM-VIII-IX, October 2021 15
Figure11. The Sequential Results of the Pass Band and Final IIR Filter Using Stop Band for De Noising
It is clear from the Figure 10 that as in notch filter the 3 poles lies in right side thus it tends towards instability. For IIR filter the all the poles and zeros lies on the left hand side thus makes it stable. While in proposed reduced order filter two poles lies in left and one on origin thus this is the most stable case of the all. But it is to observe the amplitude of two poles is more than 1 for proposed filter thus it may leads to instability if not carefully designed.
The stability of the three filters is presented in the Table 2 with respect to filter order. The reduced order filter is much close to stability critter with pole at origin.
The results of the three EEG channels with proposed method of filter are presented in the Figure 11.It is clear the filtered results remove the artifacts to significant level. Both muscular EMG and eye motion EOG artifacts are simultaneously removed by the proposed method. Although only concern is that due to reduced order filter design the amplitude of the filtered signal is also attenuated greatly. Thus these filter design needs the amplifiers to boost the magnitude of signal.
The eye blink magnitude is cut down from more than 800 to 100 range for EEG ch-9 and for EEG Ch-13 magnitude cuts to 100 from around more than 1000. These results are clear from the Figure 11. And justify the reduction in artifacts effect in EEG data.
6. CONCLUSIONS AND FUTURE SCOPE
Currentpaper has presented the results for the EEG signals artifact removal method based on the designing of efficient reduced order optimum IIR filter design. The filter is designed using the two stage IIR filter optimization using Min-Max optimization. The step response of the designed filters are evaluated for the performance of Notch filter designed at 8th order , IIR filter designed at 16th order, and the proposed 2nd order IR filter. The three EEG channels as Ch-9, Ch-4, and the Ch-13 were used for representing the filter performance.
The results are visually and qualitatively evaluated. It is clear from the results that the noisy artifact signals are efficiently removed by reduced order optimum IIR filter design.The stability is evaluated using the step response and the pole zeros analysis. It is found that the stability is good for proposed method.
Overall paper presets significant contribution and the good evaluation of the stability criterion of the designing an efficient reduced order IIR filter for EEG artifact removal In future stability improvement methods can be used for better filter performances.The hardware structure can be considered for the evaluations in future.
ACKNOWLEDGMENT
Author acknowledge to each individual contributing to this research and also to all authors and co authors referred.
0 500 1000 1500 2000 2500 3000
-1000 0 1000
0 500 1000 1500 2000 2500 3000
-200 0 200
0 500 1000 1500 2000 2500 3000
-1000 0 1000 2000
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