TABLE OF CONTENTS We live in an analog world, in that the signals that interest us are typically continuous. Our computers are digital devices, meaning that they can store only finite, discrete data, limited in both precision and magnitude. Thus, we need to approximate signals before we can store and manipulate them. How do we bridge the gap between the real world and the synthetic one of our computers? This chapter addresses this central question.
Sampling is the process of getting a digital signal from an analog one. When we sample a signal, we record, every so often, a value. Sampling can lead to many data values. For example, a 3-minute song, sampled at 16 bits at 44,100 Hz (for two channels), produces:
Changing the units to make them uniform makes this:
But do we really need to store 30 MB of data for a 3-minute song? Actually, there are other ways of storing this data. The MP3 format is one such solution. It is popular due to the fact that a song stored as an MP3 sounds very close to the original, while only requiring about 10% of the space.
Converting an analog signal to a digital one is a necessary step for a computer to analyze a signal: modern computers are digital machines, and can store only digital values.
In the continuous function x( t), we replace t, the continuous variable, with nT s, a discrete value. We use n to...
