Biomedical Signal Processing

Introduction

Biomedical signal processing is where signals and systems theory literally saves lives. Every heartbeat you see on a hospital monitor, every brain scan that detects epileptic activity, every muscle signal that controls a prosthetic limb — all of these rely on the fundamental concepts of filtering, spectral analysis, and system characterization that we study in this course. As a B.Tech student, understanding biomedical signals gives you a powerful appreciation of how abstract mathematical tools translate into real-world impact.

The human body is essentially a complex system that generates electrical, mechanical, chemical, and acoustic signals. These signals carry vital diagnostic information, but they are often weak, contaminated with noise, and buried within other physiological activity. Our job as signal processing engineers is to extract meaningful information from these challenging signals.

Types of Biomedical Signals

Electrocardiogram (ECG/EKG)

The ECG records the electrical activity of the heart through electrodes placed on the skin surface. A typical ECG signal has:

• Amplitude range: 0.5 to 5 mV
• Frequency range: 0.05 to 100 Hz (diagnostic bandwidth)
• Key features: P wave, QRS complex, T wave, with the R-peak being the most prominent

The QRS complex represents ventricular depolarization and has a duration of 60–100 ms. The heart rate can be calculated from the R-R interval:

$$\text{Heart Rate (bpm)} = \frac{60}{T_{R-R} \text{ (seconds)}}$$

Electroencephalogram (EEG)

The EEG measures brain electrical activity through scalp electrodes. It is characterized by:

• Amplitude: 10 to 100 µV (much weaker than ECG)
• Frequency bands: Delta (0.5–4 Hz), Theta (4–8 Hz), Alpha (8–13 Hz), Beta (13–30 Hz), Gamma (30–100 Hz)
• Applications: Sleep studies, epilepsy detection, brain-computer interfaces

The power spectral density of EEG in different frequency bands indicates different brain states. For example, alpha waves dominate during relaxed wakefulness with eyes closed.

Electromyogram (EMG)

EMG records muscle electrical activity:

• Amplitude: 50 µV to 5 mV (surface EMG)
• Frequency range: 20 to 500 Hz
• Applications: Prosthetic control, rehabilitation, neuromuscular disorder diagnosis

The root-mean-square (RMS) value of EMG correlates with muscle force:

$$\text{RMS} = \sqrt{\frac{1}{N}\sum_{n=0}^{N-1}|x[n]|^2}$$

Noise Sources and Removal

Common Noise Sources

Biomedical signals are plagued by several noise sources:

1. Power line interference (50/60 Hz): Electromagnetic coupling from mains power creates a strong narrowband interference
2. Baseline wander: Low-frequency drift (< 0.5 Hz) caused by respiration and body movement
3. Muscle artifacts: High-frequency noise from nearby muscle activity
4. Electrode motion artifacts: Transient disturbances from electrode-skin interface changes

Filtering Strategies

Notch filter for power line removal: A second-order IIR notch filter centered at 50 Hz (or 60 Hz):

$$H(z) = \frac{1 - 2\cos(\omega_0)z^{-1} + z^{-2}}{1 - 2r\cos(\omega_0)z^{-1} + r^2 z^{-2}}$$

where $\omega_0 = 2\pi \times 50/f_s$ and $r$ (close to 1) controls the notch bandwidth. A narrower notch (larger $r$) removes less of the desired signal.

High-pass filter for baseline wander: A Butterworth high-pass filter with cutoff at 0.5 Hz removes slow drift while preserving the ECG P wave.

Low-pass filter for high-frequency noise: A cutoff at 40–100 Hz (depending on application) removes muscle artifacts from ECG.

Adaptive filtering: When a reference noise signal is available (e.g., a separate electrode measuring mainly noise), an adaptive filter using the LMS algorithm can subtract interference:

$$w[n+1] = w[n] + \mu \cdot e[n] \cdot x_{ref}[n]$$

where $\mu$ is the step size and $e[n]$ is the error signal.

ECG Signal Processing: A Detailed Example

QRS Detection (Pan-Tompkins Algorithm)

The Pan-Tompkins algorithm is the gold standard for R-peak detection:

1. Bandpass filter (5–15 Hz): Maximizes QRS energy while rejecting P/T waves and noise
2. Differentiation: $y[n] = \frac{1}{8T}(-x[n-2] - 2x[n-1] + 2x[n+1] + x[n+2])$ — enhances the steep slope of QRS
3. Squaring: $y[n] = x[n]^2$ — makes all values positive and amplifies large slopes
4. Moving average integration: $y[n] = \frac{1}{N}\sum_{k=0}^{N-1}x[n-k]$ — smooths the result into a pulse corresponding to each QRS complex
5. Adaptive thresholding: Dual thresholds that adapt to signal amplitude for robust detection

Heart Rate Variability (HRV) Analysis

Once R-peaks are detected, the sequence of R-R intervals forms a new signal that can be analyzed:

• Time-domain metrics: SDNN (standard deviation of R-R intervals), RMSSD (root-mean-square of successive differences)
• Frequency-domain analysis: Power spectral density of R-R interval series reveals autonomic nervous system activity
• Low frequency (LF: 0.04–0.15 Hz): Mix of sympathetic and parasympathetic activity
• High frequency (HF: 0.15–0.4 Hz): Parasympathetic (vagal) activity
• LF/HF ratio: Indicator of sympathovagal balance

Spectral Analysis of Biomedical Signals

The power spectral density is fundamental in biomedical signal analysis:

$$S_{xx}(f) = \lim_{T \to \infty} \frac{1}{T}|X_T(f)|^2$$

In practice, we use Welch's method — dividing the signal into overlapping segments, windowing each, computing the FFT, and averaging the periodograms. This reduces variance of the spectral estimate at the cost of frequency resolution.

For EEG analysis, the relative band power is computed as:

$$P_{\text{band}} = \frac{\int_{f_1}^{f_2} S_{xx}(f) \, df}{\int_{0}^{f_s/2} S_{xx}(f) \, df}$$

Wavelet Analysis in Biomedical Applications

The wavelet transform is particularly suited to biomedical signals because they are non-stationary (their frequency content changes over time). The continuous wavelet transform:

$$W(a, b) = \frac{1}{\sqrt{|a|}} \int_{-\infty}^{\infty} x(t) \psi^*\left(\frac{t-b}{a}\right) dt$$

provides simultaneous time-frequency localization. Common wavelets used include the Daubechies wavelet (for ECG denoising) and Morlet wavelet (for EEG time-frequency analysis).

Applications and Clinical Impact

• Cardiac monitoring: Continuous ECG analysis in ICUs detects arrhythmias in real-time
• Brain-Computer Interfaces (BCI): EEG signal classification enables paralyzed patients to control devices using thought
• Sleep staging: Automated analysis of EEG/EMG/EOG classifies sleep stages
• Fetal monitoring: Extraction of fetal ECG from maternal abdominal signals using adaptive filtering and blind source separation
• Hearing aids: Real-time noise reduction and speech enhancement using spectral subtraction and beamforming

Key Takeaways

• Biomedical signals are weak (µV to mV range), noisy, and non-stationary, requiring specialized processing
• Common filtering: notch filters for power line noise, bandpass for feature enhancement, adaptive filters for artifact removal
• The Pan-Tompkins algorithm demonstrates a complete signal processing pipeline for QRS detection
• Spectral analysis (PSD, band power) reveals physiological states in EEG and HRV
• Wavelet transforms provide time-frequency analysis essential for non-stationary biomedical signals
• Real-time processing constraints are critical in clinical monitoring applications