# What are features in signal processing using a more tangible or less abstract description

I'm learning about signal processing for music, and in my reading I keep finding the term "features". I find that they never really give a concrete example of what they mean by "features". They'll say stuff like features related to timbre, but they won't really go into further depth than that. I also took an image processing class once and found that I didn't really understand it there either. I understand what some literal features of a sound would be, like say distortion, but I have a feeling that this isn't really what they're talking about when they say features.

Example

I'm reading something on Dynamic Time Warping(an algorithm that seems similar to local/global alignment) and they say this

To compare two different features x, y ∈ F, one needs a local cost measure, sometimes also referred to as a local distance measure, which is defined to be a function c :F×F → R.

My understanding of Dynamic Time Warping is that two similar waves(∿), aligned to each other by measuring the distance between each subsection of one wave to each subsection of the other wave and then choosing the alignment that minimizes the total distance between all the wave sections. I'm doing this for soundwaves, so why are they describing it as comparing two different "features"?

Obviously it can't be described in a way that is 100% tangible, but I'm looking for a description of features that one would be able to draw out or make a picture of.

A feature is a number that describes one aspect of a signal.

Signals can be very complex, and the simplest analysis tools (like a time plot, a spectrum, or an energy measurement) don't tell you everything; in fact, for specific types of analyses, they almost don't tell you anything useful.

So, features are designed to describe very specific aspects of a signal.

To make an analogy, let's say you're an expert in ice cream and want to compare two brands. Just looking at a picture or the list of ingredients is not enough. You can taste them, but you can't accurately describe the taste to your colleagues (just like you can listen to sound but you can't describe exactly what it sounds like).

So, you come up with "features" about the ice cream: the density, the statistics of the nitrogen bubbles inside it, the sugar/fat ratio, the crystalinity, whatever. Some of the features will be useless, but some will turn out to be really good at objectively conveying something interesting about ice cream.

• And so how exactly are you able to take numbers from the signal which you know represent these features. My confusion is it seems like your just taking some numbers, turning them into some other numbers, and saying 'These are the "features"' – Sam Jan 23 at 22:53
• How exactly -- often it's more an art than a science. To see how it's done exactly, you can dive into library code (for example, librosa) or journal papers. And yes, you're taking numbers and turning them into numbers, but sometimes those numbers tell you something useful. – MBaz Jan 23 at 23:05
• I feel like that's really the point here - a signal is really just a continuous line or a discrete sequence of numbers (might be 1D, 2D, 4000D, whatever). A feature is a number calculatable from these numbers that describes a property. That property can be very tangible and hard to calculate – say an average perceived loudness of an audio signal, which requires a psychoacoustic model – or tangible and easy to calculate – say average tide lift from a water level sensor data stream – or completely without specific meaning – like feature number 12148 in Google's neural network categorizing images – Marcus Müller Jan 23 at 23:25
• And that's it. It's a number that describes a signal, and isn't the signal itself. Different "problems" call for different features and methods of finding features. Basically, all of machine learning classification is an algorithm that tries to find features according to which you can decide whether something belongs to a class; be it images that might contain cats, or audio that might contain enemy communication, or radio signals that might contain messages from extraterrestrial intelligence. – Marcus Müller Jan 23 at 23:26