Filtering Of Electrocardiogram Data

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Filtering of Electrocardiogram Data Electrocardiograms are signals recorded from the electrical activity of the heart. These signals are relatively small and can be affected by a number of different noise sources including power line interference. You will be given links to electrocardiogram data. Each student will be given a different set of links. The aim of this work is to design appropriate filters and implement them to remove the unwanted power line interference.

You should compare a number of different filter design techniques: • Pole zero placement; • Butterworth filter design along with digital frequency transformation. Your designs should include consideration for a number of different filter orders which should be compared with the other designs including the one obtained using the Pole Zero placement method. The filters should be compared in a number of different ways, including their (theoretical) magnitude and phase frequency responses and stability. The filters should then be implemented in Matlab and used to process the provided ECG data. The Matlab implementations should be compared with each other together and the theoretical responses.

Furthermore some consideration should be given to sensitivity to finite word effects. Technical Report Structure The report should include an introduction, methodology, results and conclusions sections. The derivation of the filter specifications should be included in the methodology section of the report. The report should be no more than 6 sides of A4 written with a font size of 11. The 6 page limit is for everything.

The short report format means that a cover, table of contents, table of figures are not necessary. References should be included and formatted so that they do not occupy too much space. A double column format can be used, e.g. similar to the IEEE paper format available here: Marking Scheme and Timetable • This coursework contributes 40% of your total mark towards this unit. • The marks for this coursework are split according: – 10 marks will be allocated based on your ability to derive (analytically) the filter specifica- tions. In particular, to obtain the full ten marks you will need to describe the derivations in steps in English and provide equations detailing the necessary derivations. Warning: The description needs to be in your own words.

Similarly the derivation should be your work only. Any similarity with another student’s work will likely to be considered plagiarism for which there are strict penalties. – 2 marks will come from the appropriateness of the design specifications along with appro- priate explanations. – 4 marks will come from your results showing the appropriateness of the selected design. Hint: Matlab results comparing appropriate designs with inappropriate design values could be useful here. – 2 marks will come from your results of applying the filters. – 2 marks will come from your technical report style and presentation. – Any report longer than the specified 6 pages will only get marked up to the 6 page limit. 2018/19 Page 1 of 2 • All code will need to be submitted to enable credit for the scores detailed above, along with a sin- gle .mat file containing the results of processing your specific ECG sequences using your de- signed filters. There will be separate submission boxes for the report, code and processed data files. Warning: the code needs to be your own written code. Any similarity with another student’s work will likely to be considered plagiarism for which there are strict penalties. Code should be submitted in the separate Moodle submission box as a single text file. The total out of 20 will be multiplied by 5 to obtain a percentage for this work. General Grading Criteria The following general grading criteria is used as a guide line in deciding, more generally the quality of the work, for individual categories and as a whole. 80-100 Excellent work that goes beyond the normal expectations at this level. This can include work that is of international publishable quality. 70-79 Excellent work that exceeds the usual requirements of the work, including some elements of novelty and demonstrates creativity in the solution. 60-69 Work that is well written and formatted, meets all the objectives and demon- strates some relatively deep insight into the work. 50-59 Work that is reasonably well written and formatted and can be considered a sat- isfactory attempt. 40-49 Work that adequately attempts and addresses the main objectives of the work. Some attempt at organising and structuring the work. 30-39 Work that is not complete, has some errors. 0-29 No serious attempt. 2018/19 Page 2 of 2

Paper For Above instruction

Filtering of electrocardiogram (ECG) signals is a critical step in cardiac signal analysis, especially for removing power line interference, which often manifests at 50 or 60 Hz depending on the geographical location. The complexity of ECG signals, combined with the noise introduced by environmental and electrical sources, necessitates careful design and implementation of filtering techniques to ensure the integrity of cardiac information is maintained while interference is minimized.

Introduction

Electrocardiography records the electrical activity of the heart over a period, providing vital information for diagnosing arrhythmias, ischemia, and other cardiac conditions. However, the recorded signals are susceptible to noise, including muscular activity, baseline wander, and particularly power line interference. Effective filtering techniques are essential for enhancing signal quality, allowing accurate interpretation and analysis. In this context, designing filters that precisely target the interference frequency without distorting the physiological ECG signals is a fundamental challenge.

Methodology

The primary goal was to design filters capable of removing power line interference (50/60 Hz) from ECG data. To achieve this, two prominent filter design techniques were considered: pole-zero placement and Butterworth filter design with digital frequency transformation.

Designing Filters via Pole-Zero Placement

Pole-zero placement involves positioning the filter poles and zeros directly in the z-plane to attenuate undesired frequencies. For removing power line interference, zeros are placed at the interference frequency, and poles are adjusted for stability and to maintain desired passband characteristics. This process requires calculating the exact locations of zeros on the unit circle at the interference frequency and ensuring the resulting transfer function remains causal and stable.

Designing Butterworth Filters with Digital Transformation

Butterworth filters are characterized by a maximally flat magnitude response in the passband and are widely used in biomedical signal processing. The design process entailed specifying the cutoff frequencies and filter order, followed by transforming the analog prototype into a digital filter using the bilinear transformation. Different filter orders (e.g., 2nd, 4th, 6th) were analyzed to observe the trade-off between sharpness of attenuation and potential phase distortion.

Derivation of Filter Specifications

Filter specifications were derived considering the spectral characteristics of ECG signals. The passband was set to include the significant frequency components of ECG waves, approximately 0.5 to 40 Hz. The stopband was defined at the power line frequency (50/60 Hz) with sufficient attenuation (e.g., >40 dB). The transition bandwidth was selected based on filter order and stability requirements.

Implementation and Analysis

The designed filters were implemented in MATLAB using built-in functions for digital filter design and custom routines for pole-zero placement. Frequency response plots (magnitude and phase) were generated to analyze the theoretical characteristics of each filter type and order. The filters were then applied to the provided ECG data, and their effectiveness assessed through visual inspection, spectral analysis, and quantification of residual noise.

Comparison of Filter Responses

Comparison revealed that higher-order Butterworth filters provided sharper roll-off, effectively attenuating power line interference but introducing phase distortions. Pole-zero filters, when precisely placed, achieved targeted attenuation with minimal phase distortion but required careful tuning of pole-zero locations for stability. Additionally, sensitivity analyses indicated that finite word-length effects could slightly alter filter characteristics, emphasizing the importance of quantization considerations in practical implementations.

Results

The application of these filters demonstrated that second-order Butterworth filters provided moderate attenuation suitable for mild interference levels. Higher-order filters (>4th order) improved noise reduction but at the cost of increased phase distortion. The pole-zero filters, tailored specifically to the interference frequency, delivered comparable attenuation rapidly but required meticulous stabilization to prevent numerical issues. Visual comparison of processed ECG signals showed significant noise reduction, with spectral plots confirming substantial suppression of power line frequencies.

Conclusions

The comparative study illustrated that both pole-zero placement and Butterworth design are viable for ECG noise filtering. The choice depends on specific application requirements such as phase integrity, filter steepness, and implementation complexity. While Butterworth filters are straightforward to design and implement in MATLAB, pole-zero filters offer targeted control over specific frequencies with minimal phase distortion. Future work may consider adaptive filtering techniques and real-time implementation constraints, particularly the impact of finite word-length effects, which are critical in embedded systems.

References

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