Biomedical Signals and Instrumentation: Sensors, ADCs, Sampling, and Noise

Biological system

Interacting physiological components that receive inputs and generate responses.

Biosignal

Variation carrying information about a biological process.

Stimulus

Input signal directed toward a physiological system.

Response

Output generated by the physiological system.

Transducer

Device that converts one form of energy or signal into another measurable form.

Electrode

Conductive interface used to measure bioelectric potentials or deliver current.

Electrical biosignal

Information conveyed by electrical potential or current fluctuations.

Mechanical biosignal

Information conveyed by force, pressure, position, or movement.

Chemical biosignal

Information conveyed by concentration or chemical activity.

Thermal biosignal

Information conveyed by temperature variation.

ECG

Recording of the heart's electrical activity.

EEG

Recording of electrical activity associated with the brain.

EMG

Recording of muscle electrical activity.

EOG

Recording of electrical potentials associated with eye movement.

GSR

Galvanic skin response: changes in skin conductance associated with physiology.

Thermocouple

Converts a temperature difference into voltage.

Thermistor

Uses temperature-dependent resistance to measure temperature.

Strain gauge

Converts deformation into a resistance change.

Piezoelectric transducer

Converts mechanical stress into electrical charge.

Photodiode

Converts incident light into electric current.

Analog signal

Signal continuous in time and amplitude.

Digital signal

Signal represented with sampled times and quantized amplitudes.

Continuous-time signal

Signal defined at every time instant.

Discrete-time signal

Signal defined at separate indexed times.

Sampling

Taking measurements of a continuous signal at discrete times.

Quantization

Mapping continuous amplitude values to a finite number of levels.

ADC

Analog-to-digital converter; samples and quantizes analog signals.

Sampling frequency (fs)

Samples per second, in Hz.

Sampling period (Ts)

Time between samples; Ts = 1/fs.

ADC bit depth

Number of binary digits used to encode a sample.

ADC levels

An ideal b-bit ADC has 2^b distinct output codes.

ADC resolution

Nominal step size ΔV = input range/2^b (ideal convention).

Quantization error

Difference between original input and its quantized representation.

ADC accuracy

Closeness of digital measurement to the true input; not the same as resolution.

Nyquist frequency

One-half of the sampling frequency, fs/2.

Aliasing

Undersampling makes higher-frequency content appear at incorrect lower frequencies.

Anti-aliasing filter

Analog low-pass filter used to attenuate frequencies above the usable sampling band.

Time domain

Representation of signal value versus time.

Frequency domain

Representation of a signal by frequency components.

One-dimensional signal

Signal indexed along one independent dimension, such as time.

Two-dimensional signal

Signal indexed in two dimensions, such as image rows and columns.

Pixel

Individual discrete element of an image.

Spatial frequency

Number of spatial oscillations per unit distance.

Image thresholding

Classifying image pixels using an intensity cutoff.

Noise

Unwanted variability interfering with the desired signal.

Physiological variability

Biological changes that complicate measurement of the intended variable.

Environmental interference

Unwanted signals introduced from surrounding sources.

Measurement artifact

Unwanted signal caused by movement or unintended sensor response.

Electronic noise

Random electrical fluctuations generated within electronic components.

Gaussian distribution

Symmetric bell-shaped distribution characterized by mean and variance.

Uniform distribution

Constant probability density across a specified range.

Gaussian mean

Location parameter μ defining the center of a normal distribution.

Gaussian standard deviation

Parameter σ controlling the spread of a normal distribution.

Normal 68-95-99.7 rule

About 68%, 95%, and 99.7% lie within 1, 2, and 3 standard deviations.

Histogram

Counts or frequencies of observed values grouped into bins.

Probability density function

Function whose integral over an interval gives a continuous variable's probability.

Central Limit Theorem

Under appropriate conditions, means of many observations approach a Gaussian distribution.

Additive noise

Noise that combines with the desired signal by addition.

Thermal noise

Electrical fluctuations caused by thermal charge motion; Vrms = sqrt(4kTRB).

Shot noise

Fluctuations from random arrivals of discrete charge carriers; Irms = sqrt(2qIB).

Bandwidth

Range of frequencies admitted or analyzed by a system.

White noise

Ideal noise with flat power spectral density across frequency.

Noise reduction by filtering

Suppressing unwanted frequencies while retaining useful signal components.

Noise reduction by shielding

Reducing electromagnetic coupling from the surroundings.

Deterministic signal

Fully determined by a rule and its starting conditions.

Stochastic signal

Signal described statistically because randomness is involved.

Chaotic signal

Deterministic dynamics with extreme sensitivity to initial conditions.

Logistic map

Nonlinear recurrence x[n+1] = r*x[n]*(1-x[n]); can become chaotic.

Fractal

Structure with characteristic scaling or self-similarity across multiple scales.

Periodic signal

Repeats after period T: x(t+T)=x(t).

Aperiodic signal

Does not repeat exactly at a fixed positive period.

Transient

Short-lived event or change relative to the observation interval.

Stationary random process

Statistical properties remain invariant with time under a stated definition.

Nonstationary random process

Statistical properties change over time.

Linear system

Obeys superposition: S(ax+by)=aS(x)+bS(y).

Nonlinear system

Does not obey superposition.

Time-invariant system

Shifting the input shifts output equally without changing shape.

Time-varying system

Response depends on the absolute time of application.

Causal system

Present output depends only on present and past inputs.

Noncausal system

Output depends on future input values.

Feedback

Uses information from output to influence subsequent operation.

Feedforward

Uses anticipated inputs or disturbances without relying on output error.

Negative feedback

Tends to oppose deviations from a target value.

Positive feedback

Reinforces a deviation or response.

Superposition

Additivity and homogeneity combined.

Windkessel model

Analog model of vascular resistance and compliance in circulation.

Muscle analog model

Approximation using force-generating, elastic, and viscous elements.

Vergence control model

Eye movement control using feedback and possibly feedforward paths.

Mean

Average signal level; for N samples, sum(x[n])/N.

Continuous-time mean

Average over interval T: (1/T) integral x(t) dt.

RMS

Square root of the mean of squared signal values.

Discrete RMS

sqrt(sum(x[n]^2)/N).

Sinusoid RMS

For a zero-mean sine wave with peak A, RMS = A/sqrt(2).

Symmetric square-wave RMS

For alternating +A and -A, RMS = A (assuming A positive).

Symmetric triangle-wave RMS

For a linear triangular wave between -A and +A, RMS = A/sqrt(3).

DC offset

Constant amplitude added to a waveform.

Sinusoid with DC RMS

For D + A sin(ωt) over complete cycles: sqrt(D^2+A^2/2).

Variance

Average squared deviation around mean; population form uses denominator N.

Sample variance

Common unbiased variance estimate uses N-1 rather than N.

Standard deviation

Square root of variance; spread in the signal's original units.