Contents
Sampling Theorem
by
Siddharth Chaudhari (02007022)
Nishant Jain (02007024)
Abstract:
1. Initially we describe the system which is a day-to-day application of the Signals and systems concepts and mention what the inputs and outputs of the system is.2. Next, we describe what are the different stages the input undergoes and what changes undergo the raw input data till the output stage is reached. 3. We then introduce some of the concepts used in the algorithms used to further compress this audio data to smaller sizes. Some of them being the algorithms used for creating mp3,wma,qt files each having their own advantages and unique features.
4. An argument as to why digital audio is better than its analog counterpart and how it has become the inevitable choice follows
. 5. Lastly mention the properties of the system with respect to one of the inputs, the audio input. ( variation of pressure with time )
Introduction:
Sampling theorem is one of the very basic theorems in the field of digital processing and communication which has gained increasing importance of late because of its many advantages over its analog counterpart. Sampling refers to picking out values of the signal for certain values of the independent variables. It is of utmost importance that this sampling produces a signal from which we can get back the original signal. This puts some constraints on the input signal and this brings in the Sampling Theorem.Simply put the Sampling Theorem says that when sampling an analog signal the sampling frequency must be greater than twice the highest frequency component of the analog signal to be able to reconstruct the original signal from the output signal completely. Indeed most signals in nature are of analog form. But computing devices can handle only digital signals. Digital signals also occupy less space on a storage device. So digital systems are advantageous from a mechanical point of view. This requirement of converting analog to digital signals and vice versa is fulfilled by the Sampling Theorem.
A common example is that of the video recording process. The motion is captured by a video camera (camcorder) which picks out certain instances when to take the frame. The film is then played back at such a rate that for the eyes the sequence of discrete images assumes the form of continuous motion. This theorem has a much higher potential than this simple example with its applications ranging from fields like wireless communication to scanning and photography i.e. wherever analog to digital conversion of signals is necessary. This theorem has proved its importance in completely diverse fields and we propose to examine the application of this theorem in more detail from a Signals and Systems point of view.
