 Welcome to the second module in this course on signals and systems. All through the first module we have been looking at signals and systems in what is called their natural domain. By natural domain we look at them with the independent variable as was there when the signal was recorded or when the signal was observed or when the signal was instituted. So, natural means the way the signal occurs in reality in practice and the system again is in the form that it occurs in the practical world. So, for example, if I were trying to deal with a speech signal, I would think of the speech signal as a function of time, the natural variable independent variable associated with a speech signal namely time. The speech signal could have been recorded as voltages in a recorder as a function of time or currents whatever it could be and the natural independent variable here is time. Now, one might process the speech by using an appropriate system. The word appropriate is very loaded quote unquote loaded here. What do you mean by appropriate? Appropriate means that it does what you want it to and what you wanted to do itself is a tricky thing to specify in the natural domain. For example, if you wish to separate male and female voices from a chorus which is being sung together by some male singers and some female singers. So, imagine that you have a song being sung by a few male singers and roughly an equal number of female singers. You want to separate out or emphasize the male voices in one channel and the female voices in another channel. This is what you might call a qualitative description of what you want the system to do. So, you have the signal, the musical or audio signal in the natural domain namely as a function of time and you want to put this through a system which separates out these two kinds of voices. Now, qualitatively this description is easy to understand. However, what exactly do you mean by separating male and female voices? When it comes to a system description that is not easy to understand unless we now work through the current module. We need to have a slightly broader view and vision to describe systems and in fact before we can describe systems in this broader view we need to describe signals in this broader view. So, in this module we are going to take the first step towards a change of paradigm, a change of world view in describing signals and systems and to take that step we will have to take smaller steps. We will have to begin by understanding which signals are special from the point of view of signals and systems, why are they special and what can you do with these special signals to build this quote unquote change of paradigm that we are talking about. So, let us answer this question first, which signals are special in other words which are these signals which will allow us a change of paradigm, a different way of looking at signals and systems fundamentally. Now, to answer that question let us go to the ideal voltage generator that we often encounter in high school. So, let me draw the situation, you see ideal voltage generator if you call it that would have a circular structure rotating in a magnetic field. So, you see what is important is to visualize here a rate of change of flux. So, let us assume you have a magnetic field coming out of this paper. So, you know you could show the magnetic field with dots or crosses. So, you have a magnetic field coming in or going out of this page and you have this coil. The coil changes orientation with respect to the magnetic field. So, you can visualize it rotating along one of the axis that would allow it to change that orientation. So, let us assume the coil has an area of A and let us assume that we have roughly uniform strength magnetic fields here as a function of area and let that strength be B. The coil rotates so as to change its relative orientation and let that orientation be theta. This is the situation. So, we can now visualize we have a flux linkage you see if you have just one coil the flux linkage is B A times cosine of theta and let us assume the angular velocity of the coil is omega where upon you have theta is equal to omega times t where t denotes time. Let us denote the flux linkage by lambda where upon lambda is B A cos omega t. Now, one could use this rotation of the coil in the magnetic field by the principle of electromagnetic induction to generate a voltage across two ends of the coil at which we can tap. That is the principle of generation of the voltage supply that we receive in our residences. So, what would that be then you would have d lambda dt which is the voltage generated as a consequence of electromagnetic induction is minus B A omega sin omega t. So, note here we have a sinusoidal voltage that is kind of natural it is very common to assume the voltage to be sinusoidal. In fact, you will recall that in many basic courses on electrical engineering one talks about a sinusoidal voltage input after one has mastered the art of dealing with circuits with direct current and direct voltage. This is one important reason why the sinusoidal voltage is highly favored and deeply studied. So, I have kind of in this discussion given you a flavor of why the sinusoidal voltage has a special status. Sinusoids or sine waves have a special status in the minds of an electrical engineer and in fact, in the minds of all engineers and I have given you one reason why and of course, there are many other reasons why. Here I have given you a physical or an engineering reason why sinusoids are important. In the next discussion I am going to show you some other interesting properties of sinusoids and that is that essentially will tell us why they are also mathematically important. Thank you.