Adaptive Filtering

Prince E. Adjei

Kwame Nkrumah University of Science and Technology

Topic: Adaptive Filtering Module 2: Signal Processing

Biosignal Processes And Analysis (BME 366)

Topics:

(1). Introduction to Adaptive Filtering

(2). LMS Algorithm and Step-Size Stability

(3). Motion Artifact Removal Using Accelerometer Data

(4). Adaptive Noise Cancellation for Fetal ECG Extraction

(5). Block LMS (BLMS) vs LMS: Convergence and Efficiency

Adaptive Filtering

Learning Objectives

•Explain the concept and applications of adaptive filtering in

biomedical signals.

•Apply the LMS algorithm; analyze the impact of step size.

•Use accelerometer signals with adaptive filtering to remove motion

artifacts.

•Compare Block LMS and standard LMS in terms of convergence and

efficiency.

•Design an adaptive noise canceller to extract fetal ECG and

evaluate its performance.

Adaptive Filtering

•Adaptive filtering is a digital filtering technique where the filter

automatically adjusts its internal parameters over time.

•Unlike fixed filters, it can respond to changes in the signal or

noise characteristics.

•Designed to minimize an error signal, often by comparing the

filter output to adesired reference.

•Uses algorithms like LMS or RLS to update filter weights.

•Reduces noise or extracts useful components dynamically.

Motion-artefact anatomy

•Motion artefacts distort ECG signals due to movement (e.g.,

walking, shifting electrodes).

•These artefacts often cannot be removed by fixed filters

because they overlap with ECG frequencies and do not change

over time (non-stationary)

•However, they are often correlated with accelerometer signals

from wearables.

Adaptive filters can track and cancel this noise in real time by:

•Taking the accelerometer signal as a reference.

•Dynamically adapting to the noise pattern.

•Subtracting motion-related components from the ECG.

Motion-artefact anatomy

•LMS (Least Mean Squares) is an adaptive algorithm that updates

filter weights to minimize the error between the desired signal and

the filter output.

Weight-Update Rule

Where:

•w[n] = filter weights at time n

•μ= step size (learning rate)

•e[n]=d[n]−y[n] = error between desired signal and filter output

•x[n] = input signal vector

LMS Algorithm

•The step size, denoted by μ, controls how fast the adaptive filter

updates its weights.

•Small μ:Slow learning, but stable and precise.

•Large μ:Fast learning, but can overshoot and become unstable.

•Choose μto balance speed and stability

•Rule of thumb:

Step size in LMS

Demo: LMS on noisy wrist ECG

•A variation of the LMS algorithm where updates are done in blocks

rather than sample-by-sample.

•Faster convergence: Updates weights using information from a full

block of data.

•Better numerical stability on some systems (e.g., DSPs, GPUs).

•Useful for processing signals in batches, e.g., ECG chunks or long EMG

sequences.

Block Length Matters:

•Small block size →more frequent updates, but higher computational

overhead.

•Large block size →smoother updates, but may miss quick signal

changes.

•Trade-off between responsiveness and efficiency.

Block LMS

Demo: BLMS vs LMS convergence plot

Questions

1) What does the LMS algorithm aim to

minimize during filtering?

2) What role does the step size(μ) play

in the LMS algorithm, and how does it

affect accuracy and convergence?

3) How does Block LMS improve on the

standard LMS, and what does the

block length influence?

•In some scenarios (like fetal ECG), a clean reference signal (e.g., chest

lead for maternal QRS) isn’t available.

•Adaptive filtering needs smarter methods to still work reliably.

NLMS (Normalized LMS)

•A variant of LMS that automatically scales the step size (μ) based on

input power.

•Helps prevent instability when signal amplitude changes.

•Update Rule:

•More stable than standard LMS when signal power varies.

Reference-free adaptive tricks

RLS (Recursive Least Squares)

•An advanced adaptive filtering algorithm that minimizes the total

squared error over time, giving more weight to recent errors.

•Achieves much faster convergence than LMS or NLMS, especially in

environments where signals or noise characteristics change quickly.

•Highly effective in scenarios where the signal properties vary rapidly,

such as:

•Real-time ECG denoising

•Brain–Computer Interfaces (BCI)

•Hearing aids and speech enhancement.

Reference-free adaptive tricks

•In fetal ECG (fECG) monitoring, we place electrodes on the

maternal abdomen to measure fetal heart activity.

•However, the signal we record is a mixture of:

Abdominal ECG=Maternal ECG+Fetal ECG+Noise

•Abdominal leads capture both maternal and fetal ECG.

•Thoracic (chest) leads record mainly maternal ECG, used as a clean

reference.

Fetal–maternal ECG mixing model

Problem: The fetal ECG (fECG) is buried within the abdominal signal:

•Abdomen=Maternal ECG+Fetal ECG+Noise

•Maternal ECG dominates the signal and must be removed.

Solution –ANC Approach:

•Use the maternal chest ECG as a reference (maternal-only).

•Apply the LMS adaptive filter:

⚬Reference input: maternal chest ECG

⚬Primary input: abdominal ECG (mixed signal)

⚬LMS adapts to model the maternal component and subtract it.

•Output: cleaned fetal ECG with reduced maternal interference.

Adaptive Noise Canceller (ANC) for Fetal ECG

After extracting the fetal ECG, we need objective measures to evaluate

signal quality and clinical usefulness.

Key Metrics:

•Signal-to-Noise Ratio (SNR):

⚬Measures how clean the extracted fetal ECG is.

⚬Higher SNR = less interference from maternal ECG and noise.

•Fetal Heart Rate (HR) Accuracy:

⚬Compares detected fetal beats to the true beat locations (ground

truth or clinical reference).

⚬The accuracy of heart rate estimates is critical for fetal monitoring.

Quality Metrics for fECG Extraction

Objective: Apply adaptive filtering techniques (LMS and Block LMS) to a

real-world wearable ECG dataset.

What You’ll Do:

•Load ECG recordings with motion artefacts (e.g., wrist-based ECG).

Implement:

•LMS filter to cancel noise using reference (e.g., accelerometer or chest

ECG).

•Block LMS (BLMS) for faster convergence and efficiency.

Compare results:

•Evaluate noise reduction, convergence, and fetal signal clarity

Lab Preview: LMS & BLMS on Wearable ECG

•Adaptive filters are essential when signal conditions change over time,

making fixed filters ineffective.

•The Least Mean Squares (LMS) algorithm updates weights iteratively to

minimize the error between desired and actual outputs.

•Filter performance depends on careful selection of parameters like step

size, which affects both stability and convergence speed.

•Advanced variants like Block LMS and Normalized LMS improve

convergence and robustness under varying signal conditions.

Summary