 A warm welcome to this course on Digital Signal Processing, let me first introduce myself. I am Vikram M. Gadre a professor in the department of electrical engineering at IIT Bombay. And I am going to be the principal instructor of this course, I will explain why I say principal instructor because there are many others who have been involved in the creation of this course besides me. First about the course, the words digital signal processing are suggestive. In fact, let us take each of the words in turn starting from processing. Processing means some kind of modification or extraction that is what we mean by processing. So, what are we processing here we are processing signals. And what kind of signals are we processing digital signals? Signals that are indexed by the integers, they are discrete in the independent variable. For example, they could have come as samples of an audio signal, they could have come as samples of an instrumentation signal, they could have come as image picture elements or going further even volume elements in a 3 dimensional kind of pattern. So, when you say discrete signal here, it could be 1 dimensional, it could be 2 dimensional, it could be multidimensional. Of course, we will most the time focus on 1 dimensional signals in this course. Why would you want to process such signals because analog processing that means processing the continuous signal itself like for example, in the context of audio or speech is not always very economical in hardware or for that matter even in the associated software. So, sampling it and processing it brings several virtues. One of them is flexibility in the kind of processing that you do much more richness in the kinds of operations that you can do. So, it is robust, it is flexible, it is adaptable and with the advent of very high end computers today, it is extremely attractive because it allows you to use all the power of the computer to process an analog signal which otherwise in hardware could be an extremely arduous task. So, in many ways digital signal processing gives you much more power to deal even with analog signals although it is not always from an analog signal that we derive the discrete sequence that we are dealing with, this at a conceptual level what the subject is all about. Now, where is it used? I have given you the examples of audio, I have given you the examples of image, image processing, video processing, digital communication, biomedical instrumentation, field instrumentation of all kinds and today digital signal processing is also used by several other engineering disciplines mechanical engineering, civil engineering and what have you. I have even known of digital signal processing to be used by the financial analysis systems today. So, there is a good reason to learn and master the subject. Now, as far as the academic status of the subject is concerned, I am aware that in several institutions it is seen as either a core subject or a preferred elective in an undergraduate program in electrical engineering, electronics and telecommunication, instrumentation and several other life disciplines including computer science and engineering. Now, coming to the pedagogical aspect that I would like to highlight in the way we bring this course before you, this course has been created of course with me as the principal instructor as I said, but then I have with me several of my undergraduate students spanning two years, two consecutive years and what is more interesting is that I also have an association here with faculty and students of a reputed institute in Maharashtra namely GH Raishwani College of Engineering Nagpur which institute very kindly agreed to collaborate with me in the creation of this course. So, this is a pedagogical experiment with a four point kind of involvement. A faculty member from IIT Bombay, faculty members from GH Raishwani College of Engineering, students from IIT Bombay and students from GH Raishwani College of Engineering. A pedagogical experiment in that we thought it is a good idea to bring the stakeholders into the creation of the course so that we are sure the stakeholders in the long run spread much farther and more widely in the country would find the course useful and we definitely wish and hope that you enjoy this course, we all look forward to working with you as you learn the subject. Thank you so much.