A signal is simply a way to carry information. Think of the sound waves from your voice, the temperature reading on a thermostat, or the price of a stock fluctuating throughout the day. These are all signals because they represent some quantity that changes over time or space.

To work with signals, especially in electronics and computing, we first need to understand their basic properties. We can classify them into a few key pairs of types, which helps us know what tools to use to analyze or manipulate them.

One of the most fundamental ways to classify a signal is by looking at its behavior over time. Is it defined for every single instant, or only at specific moments?

A continuous-time signal exists at every possible moment in time. Imagine the temperature in a room. It doesn't jump from one value to the next; it flows smoothly through every possible value in between. You could measure it at 12:00 PM, at 12:01 PM, or even at 12:00:00.0001 seconds. There is always a value. A sound wave traveling through the air is another perfect example.

A discrete-time signal, on the other hand, is only defined at specific, separate moments. Think of the daily closing price of a stock. You get one value for Monday, one for Tuesday, and so on, but there's no defined value between those closing times. Digital audio is another example. A computer stores a song as a long list of numbers, each representing the sound level at a precise instant. There's no information between these points.

Another way to categorize signals is by whether they repeat. A periodic signal is one that repeats a pattern over a fixed duration. The swinging of a pendulum, the daily cycle of sunrise and sunset, or a perfect musical note held steady are all periodic.

The smallest part of the signal that repeats is called a cycle, and the time it takes to complete one cycle is the period, denoted by $T$. Mathematically, a signal $x(t)$ is periodic if there's a period $T$ for which this equation holds true for all time $t$:

An aperiodic signal (or non-periodic signal) does not repeat. Most signals in the real world fall into this category. A snippet of human speech, the crashing of an ocean wave, or the flicker of a candle flame are all aperiodic. They may have patterns, but not ones that repeat identically forever.

Finally, we can classify signals based on their predictability. A deterministic signal is one whose value can be predicted with complete certainty at any point in time. It can usually be described by a mathematical formula. For example, a perfect sine wave generated by an equation is deterministic. If you know the formula, you know its value at any future time.

A random signal, on the other hand, cannot be predicted precisely. Its value at any given time is subject to chance. While we can't know its exact value, we can often describe its behavior statistically, such as its average value or how much it tends to vary. The static or hiss you hear from an untuned radio is a classic example of a random signal, often called noise. Stock market fluctuations and the electrical signals in your brain are also considered random signals.

Now that you've got the basics down, let's test your knowledge.