Lecture 2, Signals and Systems: Part 1 | MIT RES.6.007 Signals and Systems, Spring 2011

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In the last lecture, I introduced and illustrated the kinds of signals and systems that we'll be dealing with throughout this course. In today's lecture, I'd like to be a little more specific and in particular talk about some of the basic signals, both continuous time and discrete time, that will form important building blocks

as the course progresses. Let's begin with one signal, the continuous time sinusoidal signal, which perhaps you're already somewhat familiar with. Mathematically, the continuous time sinusoidal signal is expressed as I've indicated here. There are three parameters, A, omega zero, and phi. The parameter A is referred to as the amplitude, the parameter omega zero as the

frequency, and the parameter phi as the phase. And graphically, the continuous time sinusoidal signal has the form shown here. Now, the sinusoidal signal has a number of important properties that we'll find it convenient to exploit as the course goes along. One of which is the fact that the sinusoidal signal is what is referred to

as periodic. What I mean by periodic is that under an appropriate time shift, which I indicate here as T zero, the signal replicates or repeats itself, or said in another way, if we shift the time origin by an appropriate amount T zero, the smallest value of T zero being referred to as the period, then X of T