🦿Biomedical Engineering II Unit 4 – Biomedical Signal Processing

Key Concepts and Fundamentals

• Biomedical signals convey physiological information generated by various biological processes within the human body
• Signals can be classified as continuous-time (analog) or discrete-time (digital) depending on their nature and acquisition method
• Sampling converts continuous-time signals into discrete-time signals by capturing values at regular intervals (sampling frequency)
• Quantization assigns discrete values to the sampled signal amplitudes, introducing quantization error
• Nyquist theorem states that the sampling frequency must be at least twice the highest frequency component of the signal to avoid aliasing
  • Aliasing occurs when the sampling frequency is too low, causing high-frequency components to appear as low-frequency components
• Signal-to-noise ratio (SNR) measures the strength of the desired signal relative to the background noise
  • Higher SNR indicates better signal quality and easier extraction of relevant information
• Fourier transform decomposes a signal into its constituent frequencies, enabling frequency-domain analysis

Types of Biomedical Signals

• Electrocardiogram (ECG) records the electrical activity of the heart, providing information about heart rate, rhythm, and abnormalities
• Electroencephalogram (EEG) measures the electrical activity of the brain, used for diagnosing neurological disorders and studying brain function
• Electromyogram (EMG) records the electrical activity of muscles, useful for assessing muscle function and diagnosing neuromuscular disorders
• Blood pressure signals monitor the pressure within the circulatory system, including systolic and diastolic pressures
• Respiratory signals capture the breathing patterns and lung function, such as airflow, volume, and gas exchange
• Photoplethysmogram (PPG) measures blood volume changes in the microvascular bed of tissue, commonly used in pulse oximetry for monitoring oxygen saturation
• Electrooculogram (EOG) records the electrical potential difference between the front and back of the eye, used for tracking eye movements
• Galvanic skin response (GSR) measures changes in skin conductance, often associated with emotional arousal and stress

Signal Acquisition and Preprocessing

• Signal acquisition involves capturing and converting biomedical signals from analog to digital form using sensors and data acquisition systems
• Preprocessing aims to improve signal quality and prepare the signal for further analysis
• Amplification increases the amplitude of weak biomedical signals to a level suitable for digitization and processing
• Filtering removes unwanted noise, artifacts, and interference from the signal
  • Low-pass filters attenuate high-frequency components, reducing high-frequency noise
  • High-pass filters attenuate low-frequency components, removing baseline drift and low-frequency artifacts
  • Band-pass filters allow a specific range of frequencies to pass while attenuating others
  • Notch filters remove specific frequency components, such as power line interference (50/60 Hz)
• Artifact removal techniques identify and eliminate signal contamination caused by external factors (motion artifacts, electrode movement)
• Segmentation divides the signal into meaningful segments or epochs for analysis, such as ECG beats or EEG events
• Normalization scales the signal to a standard range to facilitate comparison and analysis across different recordings or subjects

Time-Domain Analysis Techniques

• Time-domain analysis examines the signal's characteristics as a function of time
• Statistical measures provide insights into the signal's properties and distribution
  • Mean indicates the central tendency or average value of the signal
  • Variance and standard deviation quantify the signal's variability or dispersion around the mean
  • Skewness measures the asymmetry of the signal's probability distribution
  • Kurtosis describes the peakedness or flatness of the signal's probability distribution
• Waveform morphology analysis studies the shape and characteristics of the signal's waveform
  • Peak detection identifies important points in the signal, such as R-peaks in ECG or spikes in EEG
  • Amplitude measurements determine the magnitude of specific waveform features (QRS complex amplitude in ECG)
  • Duration measurements calculate the time intervals between waveform events (QT interval in ECG, inter-spike intervals in neural recordings)
• Cross-correlation assesses the similarity and time delay between two signals, useful for comparing signals from different sources or time points
• Autocorrelation measures the similarity of a signal with a delayed version of itself, revealing repeating patterns and periodicities

Frequency-Domain Analysis Methods

• Frequency-domain analysis examines the signal's characteristics as a function of frequency
• Fourier transform converts the signal from the time domain to the frequency domain, representing it as a sum of sinusoidal components
  • Discrete Fourier Transform (DFT) computes the frequency spectrum of a discrete-time signal
  • Fast Fourier Transform (FFT) is an efficient algorithm for calculating the DFT, reducing computational complexity
• Power spectral density (PSD) estimates the distribution of signal power across different frequencies
  • Periodogram is a simple method for estimating PSD by computing the squared magnitude of the Fourier transform
  • Welch's method improves PSD estimation by averaging multiple overlapping periodograms, reducing variance
• Spectral analysis identifies dominant frequency components and their relative strengths
  • Band power measures the signal power within specific frequency bands of interest (alpha, beta, gamma bands in EEG)
  • Peak frequency detection determines the frequency with the highest power or amplitude
• Coherence analysis assesses the linear relationship between two signals in the frequency domain, indicating their similarity and synchronization
• Time-frequency analysis techniques, such as short-time Fourier transform (STFT) and wavelet transform, provide a joint representation of the signal in both time and frequency domains

Digital Filtering in Biomedical Applications

• Digital filters process discrete-time signals to remove noise, extract specific frequency components, or enhance signal features
• Finite Impulse Response (FIR) filters have a finite impulse response and are inherently stable
  • FIR filters are designed by specifying the desired frequency response and calculating the filter coefficients
  • Windowing methods (Hamming, Hanning, Blackman) are used to truncate the ideal impulse response and reduce spectral leakage
• Infinite Impulse Response (IIR) filters have an infinite impulse response and can be unstable if not designed properly
  • IIR filters are designed using mathematical models and approximations (Butterworth, Chebyshev, Elliptic)
  • IIR filters generally require fewer coefficients than FIR filters for similar frequency responses, making them computationally efficient
• Adaptive filters automatically adjust their coefficients based on the characteristics of the input signal and a desired output or reference signal
  • Least Mean Squares (LMS) algorithm is a popular adaptive filtering technique that minimizes the mean squared error between the filter output and the desired signal
  • Adaptive noise cancellation removes noise from a signal by adaptively estimating the noise using a reference noise input and subtracting it from the noisy signal
• Filter design considerations include the filter order, cutoff frequencies, passband and stopband ripple, and transition bandwidth
• Filter stability, phase response, and group delay are important factors to consider when selecting and designing filters for biomedical applications

Advanced Signal Processing Algorithms

• Wavelet transform provides a multi-resolution analysis of the signal, decomposing it into different frequency bands and time scales
  • Discrete Wavelet Transform (DWT) computes the wavelet coefficients using a set of scaling and wavelet functions
  • Wavelet denoising removes noise from the signal by thresholding the wavelet coefficients and reconstructing the signal
• Empirical Mode Decomposition (EMD) decomposes a signal into a set of intrinsic mode functions (IMFs) that represent different oscillatory modes
  • Hilbert-Huang Transform (HHT) combines EMD with the Hilbert transform to obtain instantaneous frequency and amplitude information
• Independent Component Analysis (ICA) separates a multivariate signal into statistically independent components, useful for source separation and artifact removal
• Principal Component Analysis (PCA) reduces the dimensionality of a multivariate signal by projecting it onto a lower-dimensional space while preserving the most important information
• Time-varying analysis techniques, such as time-varying autoregressive (TVAR) models and time-frequency distributions (Wigner-Ville, Choi-Williams), capture the dynamic behavior of non-stationary signals
• Machine learning algorithms, including support vector machines (SVM), artificial neural networks (ANN), and deep learning models, are used for pattern recognition, classification, and prediction tasks in biomedical signal processing

Clinical Applications and Case Studies

• ECG signal processing for arrhythmia detection and classification
  • QRS complex detection and heart rate variability (HRV) analysis
  • Atrial fibrillation detection using time-frequency analysis and machine learning
• EEG signal processing for epilepsy diagnosis and brain-computer interfaces (BCI)
  • Seizure detection and prediction using wavelet transform and support vector machines
  • Motor imagery classification for BCI using common spatial patterns (CSP) and neural networks
• EMG signal processing for prosthetic control and gait analysis
  • Surface EMG feature extraction and pattern recognition for myoelectric control
  • Gait event detection and muscle activation timing analysis using EMG and inertial sensors
• Respiratory signal processing for sleep apnea detection and monitoring
  • Airflow and respiratory effort signal analysis for identifying apnea and hypopnea events
  • Oxygen saturation and heart rate variability analysis for assessing sleep quality
• Photoplethysmography (PPG) signal processing for heart rate and blood oxygen saturation monitoring
  • Peak detection and interval analysis for heart rate estimation
  • Pulse transit time (PTT) calculation for continuous blood pressure monitoring
• Fetal ECG extraction and analysis for fetal monitoring during pregnancy
  • Blind source separation techniques (ICA, PCA) for extracting fetal ECG from abdominal recordings
  • Fetal heart rate variability analysis for assessing fetal well-being and detecting distress
• Parkinson's disease assessment using accelerometer and gyroscope signals
  • Tremor detection and quantification using time-frequency analysis and peak detection
  • Gait and balance analysis using inertial sensor data and machine learning algorithms