Time-Domain Signal Analysis

Prince E. Adjei

Kwame Nkrumah University of Science and Technology

Topic: Time Domain Analysis Module 1: Time and Frequency Domain Analysis

Biosignal Processes And Analysis (BME 366)

(1). Importance of Time-Domain Features

(2). Descriptive Statistics for Biomedical Signals

(3). RMS and Peak-to-Peak Analysis

(4). Segmentation Methods in Signal Processing

(5). Noise Quantification

Topics:

Time Domain Signal Analysis

Learning Objectives

•Justify the use of time-domain features in biosignal analysis.

•Compute and visualize descriptive statistics (mean, median,

variance) on biosignal data using graphical overlays.

•Calculate RMS and peak-to-peak values, and relate them to

physiological conditions such as muscle fatigue.

•Differentiate between fixed and sliding windowing methods,

and apply segmentation using hop-size heuristics.

Review

•Noise in bio-signals refers to any unwanted interference or

disturbances that affect the quality of signals.

Types of noise

•Random noise: Unpredictable background fuzz from

electronics or digitization (Example, thermal noise).

•Physiological noise: Unwanted signals from other body

processes (e.g., breathing or eye blinks in EEG).

•Structured noise: Predictable interference with a clear pattern

(Example,50/60 Hz powerline )

Time Domain Signal Analysis

•Time domain signal analysis involves examining how the signal varies

over time.

•Time-domain features are numerical characteristics derived from the

signal’s amplitude variation over time.

•They describe the shape,energy, and structure of the signal without

converting it into the frequency or other domains.

•These features are especially useful in biomedical signal processing

(like ECG, EMG, EEG), where signals are often analyzed in real-time or

on resource-constrained devices.

Why time-domain features?

•Low computational cost –Efficient to calculate, suitable for real-

time applications and embedded systems.

•No transformation required –Unlike frequency-domain features,

no need for FFT or complex processing.

•Clinically relevant –Directly relates to physiological events (e.g.,

ECG heart rate, EMG muscle activation).

•Intuitive interpretation –Features like mean, peak, and RMS are

easy to understand and visualize.

•Robust to short windows –Can be computed over small

segments, making them responsive to changes.

Descriptive statistics

•Descriptive statistics are numerical measures that summarize and

describe the main characteristics of a dataset.

•In signal processing, especially biomedical signals like ECG or EMG,

they help you understand the shape,central tendency, and

variability of the signal over time.

•Common descriptive statistics include mean,median,variance,

and standard deviation

•The mean is ameasure of central tendency that gives the average

value of a set of numbers.

•In signal processing, it represents the average amplitude of a signal

over time and is often used to understand the baseline level of the

signal.

•For a signal x[n] with N samples:

Mean

Where:

•μ is the mean (average), N is the total number of samples and x[n] is

the signal value at index n

•The mean is sensitive to outliers —large spikes or noise can distort it.

Why use mean in signal analysis

•Represents average signal level: The mean gives a quick summary of

the signal’s typical value over time.

•Helps detect baseline drift: Changes in the mean across windows can

indicate baseline shifts, which are common in ECG recordings due to

movement or respiration.

•Estimates signal strength (EMG): For rectified EMG signals, the mean

reflects muscle activation level, helping monitor fatigue or exertion.

•Reduces random noise (averaging): Averaging multiple trials smooths

out noise and highlights consistent signal patterns.

•The median is a measure of central tendency that represents the

middle value in a dataset that has been sorted.

•It divides the signal into two halves: 50%of the values lie below it,

and 50% lie above it.

How to Calculate the Median

•Given a set of N signal values x[n], sorted in ascending order:

•If Nis odd:

Median

•If N is even:

•Robust to outliers: Unlike the mean, the median is not affected by

extreme values (spikes, noise).

•Good for artifact-prone data: In ECG, EMG, or EEG, sudden artifacts

won’t heavily distort the median.

•Useful for trend analysis: Tracking changes in median over time can

help detect drift or physiological transitions.

Why use Median in Signal Analysis

•Variance is measure of the dispersion of the data points around the

mean, calculated as the average of the squared differences from

the mean.

•In other words, it quantifies the spread or variability of the signal.

Variance

•𝒙𝒊= each signal value

•μ= mean of the signal

•N = total number of values

Variance helps differentiate active vs. resting states in biosignals.

High Variance

•Signal values fluctuate significantly

•Indicates a dynamic or noisy signal

•Example: EMG signal during muscle contraction

Low Variance

•Signal values are relatively stable

•Suggests a consistent baseline or low activity

•Example: ECG signal at rest

Interpreting Variance in Signal Analysis

Graphical overlays on ECG strip

•Root Mean Square (RMS) is a measure of the signal's power or

energy content over time.

•Used extensively in EMG to quantify muscle activation levels.

•RMS increases with muscle fatigue, effort, or stimulation.

•Example: Higher RMS in the biceps EMG during lifting indicates

more muscle recruitment.

•Mathematically :

Root Mean Squared

Peak to Peak

•Peak to peak is the difference between the signal’s maximum

and minimum values.

•Mathematically : Peak to Peak (P2P)=max(x)−min(x)

•Used in ECG to assess QRS complex strength or detect motion

artifacts.

•In EEG, it helps detect epileptic spikes or large voltage shifts.

•Example:

•A reduced P2P in an ECG may indicate signal attenuation from

poor electrode contact.

RMS & peak-to-peak

•Standard deviation measures how spread out or dispersed the values in

a dataset are from the mean (average).

•Mathematically

Where:

•𝒙𝒊= each data point, μ= mean of the data and N = number of data points

•Low σ:Data points are close to the mean →smooth, stable signal

•High σ:Data points are widely spread →signal has more variability or

noise.

Other descriptive statistics

•Skewness is a statistical measure that describes the asymmetry of a

distribution.

•Mathematically :

•Positive skew: Long tail on the right (values are concentrated on the

left).

•Negative skew: Long tail on the left (values are concentrated on the

right).

•Zero skewness: Symmetrical distribution (like a normal curve).

•Helps detect bias in signal values. For example, skewed EMG

amplitude during fatigue.

Other descriptive statistics

•Kurtosis is a statistical measure that describes the shape of a

distribution's tails about its overall shape.

•Mathematically:

•Describes the peakedness and tail heaviness of a distribution.

•High kurtosis (>3): Sharper peak, heavy tails (more extreme

values/outliers).

•Low kurtosis (<3): Flatter peak, lighter tails (fewer outliers).

•Kurtosis ≈3: Normal distribution (mesokurtic).

•Identifies signals with frequent spikes or bursts (e.g., seizure

activity in EEG).

Other descriptive statistics

1. Why are time domain features

useful in biomedical signals?

2. When is median preferred over

the mean in signal analysis?

3. What does RMS and variance tell

us about a signal?

4. What does peak to peak of a

signal measure?

Questions

Windowing and Segmentation

•Windowing is the process of breaking a long signal into smaller, shorter

segments called windows so we can analyze local behaviors within

those segments.

•Segmentation is a more semantic process —dividing a signal into

meaningful sections, often based on events or physiology.

•Biomedical signals are often non-stationary—their properties (like

frequency, amplitude, or shape) change over time.

•Helps us focus on short durations where the signal is quasi-stationary.

•Detect time-localized events like QRS complexes, muscle fatigue, or

epileptic spikes.

Fixed vs Sliding Window

Feature

Fixed Window

Sliding Window

Definition

Non overlapping segments

Overlapping segments

Use case

When events are well aligned or periodic

For continuous montoring and peak

detection

Pros

Faster computation

Better temporal resolution

Cons

May miss key transitions

More computation; redundancy possible

•Hop size is how much the window moves forward each step.

Common Rule:

•→50% overlap: balances redundancy and temporal resolution.

•Other options:

•25% hop (75% overlap): better detection accuracy

•100% hop (0% overlap): fastest, but risk of missing fast events

Hop-Size Rule of Thumb

Event Based Segmentation

•A method of dividing a signal based on the occurrence of meaningful

events, rather than fixed time intervals.

•In ECG, this typically means segmenting around R-peaks (heartbeats)

or QRS complexes.

Event-based segmentation allows:

•Focused analysis on individual events (heartbeats, spikes, bursts)

•More meaningful feature extraction

•Reduced noise by ignoring uninformative regions

Event Based Segmentation

1. Thresholding

•You set a value threshold to detect significant events.

•Useful for identifying sudden changes in the signal (like the QRS

complex).

2. Hysteresis

•Prevents false or repeated detections due to noise.

Uses two thresholds:

•Ahigh threshold to detect event onset

•Alow threshold to end the event or ignore small fluctuations

•This avoids jittery or unstable segmentation.

Event Based Segmentation

In the Pan-Tompkins algorithm, event-based segmentation is centered

on R-peaks, which are detected using:

•Slope, amplitude, and width analysis

•Bandpass filtering, differentiation, squaring, and moving window

integration.

Once R-peaks are detected, you can:

•Segment each heartbeat from one R-peak to the next (R-R interval)

•Or extract pre-R to post-R windows

These R-peaks become your anchors for event-based segmentation.

1. What is the main difference

between windowing and

segmentation?

2. Why is windowing important in

analyzing biomedical signals?

3. What does hysteresis prevent

in event-based segmentation?

Questions

Noise taxonomy

Physiological Noise

Origin: From the patient’s own body, but not from the target

organ/system.

Examples:

•Muscle activity (EMG) contaminating EEG

•Eye blinks (EOG) affect EEG.

•Respiratory movements distorting the ECG baseline

•Motion artifacts during EMG or PPG.

Challenge: Hard to remove, because it's still biological and often

overlaps with the signal of interest.

Noise taxonomy

Instrumentation Noise

Origin: From the hardware or electronics used to record the signal.

Examples:

•Thermal noise in amplifiers

•Quantization noise from ADC (analog-to-digital conversion)

•Electrode-skin impedance fluctuations

Characteristics: Typically random, but can sometimes be mitigated

by high-quality hardware and filtering.

Noise taxonomy

Environmental Noise

Origin: From the external environment, not the body or the device.

Examples:

•Powerline interference (50/60 Hz hum)

•Electromagnetic interference (from phones, Wi-Fi, fluorescent

lights)

•Movement of cables or devices causes artifacts

•Characteristics: Often structured/predictable (periodic), and

filtered using notch filters or shielding.

Quantifying Noise

Baseline Wander (BW)

Slow, low-frequency drift in the signal baseline —usually below 0.5

Hz.

Cause: Respiration, body movement, electrode shifts

Seen in: ECG, EEG

How to quantify:

•Estimate using a high-pass filter or polynomial fitting

•Measure the standard deviation (σ)or peak-to-peak of the drift

•Example: In ECG, BW can mask P-waves or distort ST segments

SNR (Signal-to-Noise Ratio): Measures how strong your desired signal

is relative to background noise.

Formula:

•Higher SNR = Cleaner signal

•Typical range in bio-signals:

⚬ECG: ~10–30 dB

⚬EEG: 0–10 dB

⚬EMG: Varies widely depending on contraction

Quantifying Noise

6 dB/Bit Rule —What Is It?

Every 1-bit increase in the resolution of an analog-to-digital converter

(ADC) improves the Signal-to-Noise Ratio (SNR) by approximately 6.02

dB.

Where:

•N = number of bits of the ADC

•1.76 dB is a constant from uniform quantization theory

In biomedical signal processing:

•You want high signal fidelity

•Low-resolution ADCs add quantization noise (discretization error)

•More ADC bits = higher resolution = less quantization noise

Quantifying Noise

Case Study: EMG Envelope Extraction and SNR Computation

•To assess muscle activity and quantify noise in an EMG signal, we

extract its envelope and compute the signal-to-noise ratio (SNR).

Steps:

•Rectify: Convert all EMG values to positive to reflect absolute muscle

activity.

•Moving RMS: Apply a moving root-mean-square window (e.g., 100 ms)

to smooth the signal and obtain the amplitude envelope.

•Log scale: Apply a logarithmic transformation to compress the range

and enhance small fluctuations.

•Compute SNR: Estimate signal power from the RMS envelope and noise

power from baseline wander (via low-pass filtering), then compute the

SNR

Higher RMS suggests stronger activation or fatigue; lower SNR indicates

more noise (e.g., from movement artifacts or poor electrode contact).

Summary

•Time-domain analysis looks at how a signal’s amplitude changes

over time —no need for frequency transforms.

•Time-domain features like mean, RMS, and variance summarize

signal behavior and are useful for pattern detection and

diagnosis.

•RMS indicates signal energy.

•Peak-to-peak gives the total signal range (max minus min

amplitude).

Summary

•Segmentation divides signals into smaller windows (fixed or sliding).

Sliding windows often use 50% overlap for smoother analysis.

•Event-based segmentation detects key signal events using

thresholds and hysteresis to avoid false triggers.

•Noise sources can be physiological (e.g., breathing), instrumental

(e.g., electrode movement), or environmental (e.g., powerline

noise).

•SNR compares signal strength to noise level. Higher SNR means a

cleaner, more usable signal.

Recommended Text

•Rangayyan, R. M. (2015). Biomedical signal analysis: A case-study approach

(2nd ed.). IEEE Press Series in Biomedical Engineering. Wiley–IEEE Press.

ISBN: 978-0-470-01139-6.

•Palaniappan, R. (2011). Biological signal analysis. University of Essex

•Delgutte B (2007). Course materials for HST.582J / 6.555J / 16.456J,

Biomedical Signal and Image Processing, Spring 2007. MIT OpenCourseWare,

Massachusetts Institute of Technology.