TABLE OF CONTENTS This chapter explains how a one-dimensional signal is filtered and sampled prior to A-to-D conversion, and how it is reconstructed following D-to-A conversion. In the following chapter, Resampling, interpolation, and decimation, on page 171, I extend these concepts to conversions within the digital domain. In Image digitization and reconstruction, on page 187, I extend these concepts to the two dimensions of an image.
| Note | My explanation describes the original sampling of an analog signal waveform. If you are more comfortable remaining in the digital domain, consider the problem of shrinking a row of image samples by a factor of n (say, n = 16) to accomplish image resizing. You need to compute one output sample for each set of n input samples. This is the resampling problem in the digital domain. Its constraints are very similar to the constraints of original sampling of an analog signal. |
When a one-dimensional signal (such as an audio signal) is digitized, each sample must encapsulate, in a single value, what might have begun as a complex waveform during the sample period. When a two-dimensional image is sampled, each sample encapsulates what might have begun as a potentially complex distribution of power over a small region of the image plane. In each case, a potentially vast amount of information must be reduced to a single number.
Prior to sampling, detail within the sample interval must be discarded. The reduction of information prior to sampling is prefiltering. The...
