# Confused in difference between sequence versus signal?

I am learning basics of signals and systems with MATLAB If i create a vector in matlab such that x=[ 2 5 10 20], will it be considered a sequence or a signal?

As far my learning/knowledge is, x is a sequence in this case, since it is using discrete numbers as its elements.

If there was x such that x=sin(t) or cos(t) or exp(t),it would be a signal because of the continuous range of values in it.

Please correct/guide me if i am wrong

• Signals are mathematical functions. For discrete-time functions (signals) mainly the term sequence is used. – Fat32 Apr 16 '19 at 11:20
• Did you find inspiration in the answers given? – Laurent Duval Apr 23 '19 at 17:47

To me, borrowed from the mathematical term, a sequence denotes an enumerated set of elements of the same family. By "enumerated", one understands that they can be indexed with a particular order, either by the first integers only (a finite sequence) or all integers ($$\mathbb{N}$$ or $$\mathbb{Z}$$ for bi-infinite sequences). Due to the natural ordering of the indices, sequence thus possesses both a 1D, sorted and a discrete (in the ordinal variable, or index) structure. The family of elements (e.g. their value: integers, reals or complex, categorical, etc.) does not matter, as long at all elements live in the same set.

Matt L.'s answer is quite complete on discrete/continuous signals. I would just like to emphasize that signals can be multidimensional, with an order across each dimension, but not specifically across all dimensions: a 2D satellite image does not induce an order across the 2D spatial dimensions.

So in a DSP context, I'd consider the term signal to be more generic (albeit less precise). Here, you have both a (discrete) sequence of discrete values (by chance, up to numerical approximations), and a representation of a signal (of finite length, regularly sampled, with finite non-negative integer values.).

In DSP we use the term signal to denote continuous-time functions as well as discrete sequences. To avoid confusion you can use the terms continuous-time signals and discrete-time signals.

Of course, the independent variable doesn't have to be "time" (e.g., in image processing). In that case you would simply be talking about continuous or discrete signals.

Note that often you would come across the terms analog or digital signals for continuous-time and discrete-time. That categorization is a bit more ambiguous because by digital we usually mean that not only the independent variable (often "time") is discrete but also the signal values, i.e., that the signal is quantized. But in practice it's not always clear if digital is used in that strict sense. So if you don't want to restrict yourself to quantized sequences, it is advisable to use discrete(-time) instead of digital.

Take a look at this question and its answers for more details on the distinction continuous/discrete and analog/digital.