In the world of digital signal processing, DSP, there are two basic types of signals which are often compared and contrasted with one another: continuous signals and discrete signals.
While both types of signals exist in the real world, they each have their own unique characteristics that make them more or less suitable for certain applications.
As the name implies, continuous signals are uninterrupted. They represent data for every instant of time. While discrete signals comprise a finite number of discrete values. They represent data at a specific instance in time.
This might seem overwhelming at first, but when you break it down into simple examples, it can be much easier to understand what continuous and discrete signals are. It is important to understand this, as it is the foundation of DSP. I have covered more DSP topics in my other articles, which you can find here.
In this article, I will attempt to explain this concept in very simple terms, breaking down continuous and discrete signals into very simple terms to help you understand the fundamentals, keeping the mathematics to a minimum where possible.
I will cover:
- What is a continuous signal?
- What is a discrete signal?
- What is the difference between continuous and discrete signals?
- What are examples of continuous and discrete signals?
What Is A Continuous Signal?
As the name implies, continuous signals are uninterrupted. We can represent them mathematically as a function that is defined over some infinite interval.
A continuous signal will have data for every moment for a specified time.
For example, imagine you pluck a single electric guitar string, let it ring for 5 seconds and read the output signal. You can measure the specific amplitude of the signal for those 5 seconds.
It does not matter if you take a reading at a time interval of 1 second, 0.1 seconds or 2.23 seconds, there will be an amplitude to read as the signal is continuous over the 5 seconds.
We often find continuous signals in nature, such as temperature or pressure. While it is sometimes possible to approximate continuous signals with discrete signals, doing so can cause a loss of information.
What Does A Continuous Signal Look Like?
The following image shows a continuous signal.
If you were to take a data reading at any time interval for the shown signal, you will read data, as the signal is continuous.
For continuous signals, we represent the dependent variables as x(t). We represent the independent variable as t, which stands for continuous time.
What Is A Discrete Signal?
Discrete signals are composed of a finite number of discrete values.
Discrete signals can be represented mathematically as a sequence of numbers.
Most digital devices use discrete signals since they are better suited for electronic processing than continuous signals are. However, it is important to note that while discrete signals are digital, not all digital signals are discrete—for example, a digital image comprises pixels, which are discrete units, but the overall image is a continuous signal.
What Does A Discrete Signal Look Like?
The following image shows a representation of a discrete signal.
We can see from the above signal that the data points are specified at exact places in time. We do not have data for the points on the curve that are not marked.
With discrete signals, we specify the dependent variable of the curve as x[n] and denote the independent variable as n, which means equally spaced moments in time.
What Is The Difference Between Continuous And Discrete Signals?
The following table is a very short and simple comparison of continuous and discrete signals.
| Characteristic | Continuous Signal | Discrete Signal |
|---|---|---|
| Definition | A function defined over an infinite interval. | A sequence of values with finite spacing. |
| Representation | Function | Sequence |
| Found In Nature | Yes | No |
| Digital | No | Yes |
Continuous signals have data for every moment over a specified time, whereas discrete signals will only have data for specified moments in time.
Continuous signals are a smooth, unbroken flow of data, while discrete signals are a series of individual points.
While at university, I recall my lecturer stating that continuous signals can be thought of as a river, while discrete signals would be more like a stack of rocks. It may not be a perfect analogy, but it certainly stuck with me!
The two types of signals are often used interchangeably, but there are some key differences that set them apart.
Discrete signals are typically generated by digital devices, such as computers. They are easy to store and manipulate because they are just a series of numbers.
Continuous signals, on the other hand, are usually generated by analogue devices, like microphones or thermometers. They are more difficult to store and manipulate because they are a smooth, unbroken data flow.
One of the key differences between continuous and discrete signals is how they are sampled.
Continuous signals can be sampled at any interval, but discrete signals can only be sampled at specific intervals. This means that when you are working with discrete signals, you need to be very careful about how you sample them. If you sample a discrete signal at the wrong interval, you will miss data and your results will be inaccurate.
Discrete signals are often easier to work with than continuous signals because they are more predictable. When you sample a discrete signal, you know exactly where the data points will be. This makes it easy to store and manipulate discrete signals.
We often use discrete signals in digital applications, such as computer networks. Continuous signals are often used in analogue applications, such as audio systems.
What Are Examples Of Continuous And Discrete Signals?
While DSP theory can be very intensive (read my article about DSP difficulty here), it’s nice to have some real-world practical examples of continuous and discrete signals.
Examples Of Continuous Signals
Continuous signals can be found in nature, such as sound waves, light waves, and water waves.
- Sound
- Light
- Temperature
- Pressure
- Light
Think of any signal that is continuous and not interrupted. For example, an audio signal played by an electric guitar.
Examples Of Discrete Signals
Examples of discrete signals include sounds that have been sampled at specific intervals, digital images, and numbers that have been stored on a computer.
- Sampled sound
- Sampled temperature
- Sampled light
Think of any signal that is read at a specific instant in time. For example, if you measured the temperature in your room every hour, on the hour, then this is an example of a discrete signal.
Final Thoughts
The fundamental difference between continuous and discrete signals is that a continuous signal has continuous data over time, while a discrete signal is sampled at set intervals.
There are several key differences between continuous and discrete signals. These differences include the way they are defined and represented mathematically, as well as the properties they possess and where they naturally occur.
In general, continuous signals work better with analogue devices, while discrete signals work better with digital devices; however, there are exceptions to this rule.
When choosing which type of signal to use for a given application, engineers must carefully consider all factors involved before making a decision.
