We studied about the basics of signals and systems in this previous post: Signals and Systems Basics

In this post, we’ll dive deeper into the definition of a signal and the definition of a system – along with each one’s types.

What are signals and its types?

Signals are functions of one or more independent variables that typically carry information about a biological system or a physiological process (e.g. speech signal)

There are different types of signals (w.r.t functions). These are:

• Unit Step Function: It is zero for negative values and one for non-negative values of its input variable, often denoted as u(t).

• Unit Impulse Function: Also known as Dirac delta function, this type of signal is zero for all values except at one specific point, where it is infinite at that point and integrates to one.

• Ramp Signal: It is a linearly increasing or decreasing signal over time, typically defined by its slope or rate of change, often represented as r(t) = a * t.

• Parabolic Signal: This signal has a quadratic relationship with time, meaning its amplitude varies as a function of the square of time, often represented as p(t) = a * t^2.

• Sinusoidal Signal: It is a periodic waveform characterized by a sine or cosine function, involving oscillation with a specific frequency, amplitude, and phase, often expressed as A * sin (ωt + φ).

Signals are also grouped by classes and each class has important properties. It is worth noting that a signal can be defined using multiple classes as long as two opposing classes are not used.

The classes are:

1. Continuous-time & Discrete-time Signals

Continuous-time signals that vary with respect to time and are represented as continuous functions. (e.g. ECG). 

Discrete-time signals are sampled at specific time intervals. (e.g. digital representation of an ECG signal, where data points are collected at discrete time intervals)

• Period & Aperiodic

Periodic signals repeat their pattern at regular intervals, and their behavior is predictable over time.

Aperiodic signals do not exhibit regular repetition and lack a consistent, predictable pattern.

• Deterministic and Non-Deterministic

Deterministic signals have a known and predictable behavior that can be precisely described by mathematical equations or models.

Non-deterministic signals have inherent randomness or uncertainty, making their exact future behavior unpredictable.

• Even and Odd

Even signals are symmetric with respect to the vertical axis, meaning they satisfy f(-t) = f(t) for all t.

Odd signals exhibit rotational symmetry, where they satisfy f(-t) = -f(t) for all t.

• Real & Imaginary 

Real signals have values that belong to the set of real numbers, meaning they can be both positive and negative, with no imaginary components.

Imaginary signals are represented in terms of imaginary numbers and are characterized by having no real component, typically associated with sinusoidal signals in phasor notation.

What is a system and what are the types of systems?

A system is an interconnection network through which the signal can flow from one place to another. It can be a device, process, or mechanism.

In the context of medical diagnosis, monitoring, and treatment, systems are used to analyze, modify, or interpret signals. 

Thus, these systems can be described as:

• Static or dynamic
• Linear or nonlinear
• Time-invariant or time-varying
• Causal or non-causal
• Linear time-variant or linear time-invariant

Examples

• A digital filter used to remove noise from an ECG signal is an example of a system. The noisy ECG signal (input signal) is processed through the filter (system), resulting in a cleaner, filtered ECG signal (output signal).

• A medical imaging system, such as an MRI machine, can be considered a system. It takes in radiofrequency signals generated by the patient’s body in response to strong magnetic fields (input signals) and processes them to create detailed medical images (output signals).

Collectively, in the field of biomedical engineering, the study of “Signals & Systems” deals with the processing and analysis of signals. It involves designing systems to extract useful information from signals, enhance signal quality, or make diagnoses based on signal patterns. Engineers use various mathematical and computational tools to model, analyze, and design these systems to improve healthcare and diagnostics.