I'm Piyush and I'm a student currently pursuing Masters in Electrical Engineering.
I made this article for the The Summer of Math Exposition Contest ****by 3Blue1Brown
This article goes into electrical networks and signals, and here I talk about the similarity of signals, similarity between a DC signals, and periodic signals (or AC signals). Specifically, how does average value of any AC signal relates to a DC signal.
I hope reading this article helps you in achieving a different perspective on how we look at DC and AC signals.
I have framed my doubt into a question, which is, Why the average value of a periodic signal is also termed as the DC value of that signal?
The question means, for any given periodic signal, the average value of that AC signal its also its DC value.
I never got how an average value of a periodic signal is also its DC value, what do you mean by the DC value of a periodic or AC signal? I get that they both are represented by constant or single value, contrary to AC signal who has multiple values repeating periodically.
But there was never really an illustrative way to say that average of a periodic signal is also its DC value. So here, i'd like to show you my own way of defining that.
Consider a periodic signal as shown in figure 1. The average of that signal is given by the equation 1.
Figure 1
We will get back to this later, lets focus on what is average.
Now consider a set of numbers as shown.
Now look at this part of equation, marked with green circle. Its nothing but the sum of sequence of numbers in our set.
