# What is the type of these signals?

I want to do some DSP and Machine learning experiments on Electrical and Acoustic signals, but, due to some language setbacks, I didn't know how to call the type of my signal, what I use to google now, is "Time series". Is there a more precise "key word" "terms" that may put me in the right direction?

• Can you give more details about your signals? How they are recorded, sampled? What they look like? "Time series" is fairly generic, esp. outside signal processing; "discrete signal", "discrete sequence", "discrete-time signal", "digital signal", "data frame" are options with slightly different meaning, but in the same field – Laurent Duval Jul 19 '17 at 5:04
• There was a modest repository of recorded signals at Rice when Don Johnson was IEEE Signal Processing President, which is gone but the mirrored archive is spib.linse.ufsc.br/index.html. – user28715 Jul 19 '17 at 13:25
• Thanks, Laurent Duval, my topic is electrical machines diagnosis, the current subject of interest is Partial Discharge, signals are acquired using Sensors (Hall effect, Acoustic sensors ...) ... what i really want to do, is applying machine learning algorithms, to help in localizing defects, and making prediction, so, when I google around, there are tons and tons of information, but most of them aren't related directly to my subject – Zakorakis Jul 19 '17 at 15:30

Types of signals:

• According to their range set (values): Real Valued, Complex valued ;

• According to their dimensions: Scalar, Vector ;

• According to their values: Continuous Amplitude, Quantized ;

• According to their domain set (arguments): Continuous-time, Discrete-time :

• According to their mappings: Deterministic, Stochastic (Random) ;

• According to their character: Periodic, Even, Odd, Symmetric... ;

A Time-Series is another name given to a discrete-time random sequence which is an instance of some discrete time random process. As it's a random signal, the sequence samples do not have a mathematical formula which connects the points to each other along the series, hence it's viewed as a series of numbers which were generated according to some probabilistic law.

Consider the following: You generate a continuous-time deterministic signal $x(t)$ by exciting an oscillator which produces a periodic sine wave of exactly known frequency, phase and amplitude. Then sample this signal to produce a discrete-time sequence $x[n]$. The point is that by just observing the sampled signal you cannot tell whether the sequence of samples actually belong to a deterministic signal with a mathematical formula that can be used to generate all of its samples, or they belong to a random process whose values happen to be fitting into the observed sine wave (which has a very small probability (improbable) but is not impossible otherwsie). Hence any such sequence can be considered as a random sequence of numbers denoted as a time-series.

After a certain amount of analysis you may conclude that the observed sequence of numbers probably belong to a deterministic sine wave of certain frequency,phase and amplitude. But this deduction is only an estimation. The truth cannot be known but precise predictions can be computed.

• Very interesting explanation of the schochastic character of time series, I haden't thought about it this way... Thanks! – Florent Jul 20 '17 at 2:11

There apparently exists an R package for the clustering of "Partial Discharge" data: pdCluster: Partial Discharges Clustering.

Partial discharge measurements analysis may determine the existence of defects. This package provides several tools for feature generation, exploratory graphical analysis, clustering and variable importance quantification for partial discharge signals.

This could be a starting point. In the following description, I put in bold the concept of "damped exponentials" or "damped sinusoids", that could describe the morphology of your data. This is an instance of non-stationary data.

A clean partial discharge signal can be regarded as a finite combination of damped complex exponentials. Under this assumption, the so-called Prony's method allows for the estimation of frequency, amplitude, phase and damping components of the signal.

The recent paper New clustering techniques based on current peak value, charge and energy calculations for separation of partial discharge sources, 2017, may provide other key references.