 warm welcome to this course on signal and systems. In this very first exchange of ideas between you and me, I would like to introduce to you the purpose, the contents and the manner in which this course would be conducted so that we are in sync when we proceed from the next session onwards. This course is meant to be a very fundamental course in most engineering curricula and it could also be useful to many people in the sciences domain, a very basic course. What is this course all about? It is about dealing with signals and systems. Signals essentially as we understand them in common life, they could be audio signals, they could be physiological signals recorded by electrical or other means, they could be mechanical signals, they could be acoustic signals, they could even be discrete point data signals like financial signals or economic signals. A signal is anything that indicates a function of an independent variable and we do not have great difficulty in understanding the meaning of the word signal. We use it very, we signal, you know the word signal is used both as a noun and as a verb. It is used as a noun to denote essentially a function of an independent variable. It is used as a verb when you signal somebody to convey information or to indicate that something is being communicated, something is being conveyed or someone is being alerted. A system is something that takes signals and produces signals. Let us take a few real life examples to understand what we are talking about. First let us take a mechanical system, a mass. One way to understand a mass, any mass for that matter, it could be a football, it could be a cup, it could be a lump of wood. But one common thing that all mass has is that when you apply a force on it, the acceleration is proportional to the force in a way that describes the mass. So Newton's law tells us that the force is proportional to the acceleration and the constant of proportionality is what we call the mass. Now the mass can be thought of as a system, a very simple system where you could think of the force as an input signal, the force as a function of time and the acceleration as a function of time to as the output signal. So the rate at which the velocity of the mass changes is an output here and the force is the input. Now the acceleration, in fact let us put this down mathematically. So let us denote a mass in this way. We take a square block of wood if we like and we assume that we apply a force to it which we will denote by f as a function of time, t is time. It produces an acceleration and now instead of saying acceleration, we will use the term rate of change of velocity. So the velocity of the mass, of course here I am assuming that the mass moves in a specific direction. So velocity and speed at this moment do not need to be distinguished. You see the rate of change of velocity dv dt is related to the force by f of t is m times dv as a function of t dt. This is what we call the acceleration. So this is a very simple input output system with input output signals. And let us now take another system which we know of in the electrical domain which resembles this in some way. If we for a moment look at the capacitor in an electrical system and look at the voltage across the capacitor and the current in the capacitor. Of course when I say current in the capacitor, what I mean is the rate at which the charge stored across its plates changes. And the capacitor value is C. We are very familiar with the equation. I of t is C dv dt dt. So if we take a moment to compare the mass and the capacitor, we see an analogy there. We see that in both cases one variable is related to the derivative or is proportional to the derivative of the other variable. In the case of the mass, the force is proportional to the derivative of the velocity. And the constant of proportionality is the mass. In the capacitor, the current is proportional to the derivative of the voltage. And the constant of proportionality is the capacitance itself. In both cases, we have the notion of an input and an output. Of course, you could use them interchangeably. But for the moment in the case of the mass, let us think of the force as an input and the velocity as an output, which also makes sense. And in the case of the capacitor, let us think of the current as an input and the voltage as an output. In that case, we have two very simple systems which resemble one another in behavior. And our course is going to begin with this observation that we have many systems all around us in real life which resemble one another in terms of their behavior. And what we would like to do is to capture from this resemblance what is the essence of the behavior that we want to analyze and study. Now let us take a few more examples from real life of systems and signals that accompany them. Let us take a resistance. In resistance, there is a very simple proportionality relationship. The voltage is proportional to the current or the current is proportional to the voltage either way. You see, there are systems analogous to the resistance in a mechanical or in a hydraulic context too. In fact, there are notions of viscous resistance or fluid resistance that we encounter in the mechanical context or in the hydraulic context. Let us take a slightly more complicated example. Let us take a physiological signal, the electrocardio. Here I am talking about just the signal, the electrocardiographic signal or it is called ECG in short. As many of us might know, the electrocardiographic signal is used to study the status of a person's heart, how well it functions, whether the heart seems to show any problem in terms of its functioning or if there is an indication of ill health of some kind. So, here we have a signal. I am only referring to the signal. An electrical signal which is generated as a consequence of the heart activity which can be recorded externally. And now I shall talk of a system. Suppose we had a system, suppose we took the signal in to a computer by whatever mechanism, looked at the way the signal varies in time and came to certain conclusions. Then we would be building an artificial system inside the computer which analyzes the ECG signal. So, whereas the first few examples of systems that I gave you, the mass or the capacitance were systems that you could take off the shelf. Here is a system that you need to build consciously and intelligently. A system that takes the electrocardiographic signal, processes it in some way and generates intelligent information out of it or puts out another ECG-like signal or another signal which conveys something different or which emphasizes some part of the ECG signal. All these are examples of systems that you would construct. We shall see more about these real life principles in the subsequent lecture. But I would like to conclude this first discussion that we are having with a few general remarks. I will explain to you what the purpose of this course is. It is really to understand signals and systems and to abstract from many common real life situations, a sense which you would need to understand, analyze and perhaps use later to synthesize. In short, what we are trying to do is to look at many different real life systems and signals that are associated with them, ask certain questions about those systems and those signals and it is a skill to ask the proper questions to. So, asking those questions, we should be able to address issues that relate to many systems or signals at once. That is what is called abstraction. We would like to answer those questions in this course and finally, we would like also to use these answers to be able to build systems later based on the principles that we evolved. Now, to do all this, there are some basic rules that we shall have to follow which relate to my style of exposition of this subject. In a subject like this, we do need to work together. It cannot be a one-way communication. So, I would strongly recommend that any student who works with me in this course keeps a pen and paper with him or her in front and works out a few things. It does not matter if you do not work out every little detail. But a few lines written here and there would help your thoughts to be in sync with mine. Secondly, we would work in a derivation mode. We would be writing things down. We would be working together and therefore, we would be deriving things together and that is why instead of a presentation format, I would much rather go for this kind of a format where you would write points down and build ideas one after the other. In a course like this, I believe that is more expedient rather than trying to just flash a number of ideas all at once. And of course, last but not the least, I am very happy when we get questions to answer. Please feel free to ask questions at any point as you are going along in this course and we will all be very happy to answer your questions to the best that we can. So, welcome again to this course and we shall see more about the principles on which this course is built in our next interaction. Thank you.