Basic signals FT

# Basic signals FT - Chapter 9 Basic Signal Processing...

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Chapter 9 Basic Signal Processing Motivation Many aspects of computer graphics and computer imagery differ from aspects of conventional graphics and imagery because computer representations are digital and discrete, whereas natural representations are continuous. In a previous lecture we discussed the implications of quantizing continuous or high precision intensity val- ues to discrete or lower precision values. In this sequence of lectures we discuss the implications of sampling a continuous image at a discrete set of locations (usually a regular lattice). The implications of the sampling process are quite subtle, and to understand them fully requires a basic understanding of signal processing. These notes are meant to serve as a concise summary of signal processing for computer graphics. Reconstruction Recall that a framebuffer holds a 2D array of numbers representing intensities. The display creates a continuous light image from these discrete digital values. We say that the discrete image is reconstructed to form a continuous image. Although it is often convenient to think of each 2D pixel as a little square that abuts its neighbors to fill the image plane, this view of reconstruction is not very general. Instead it is better to think of each pixel as a point sample. Imagine an image as a surface whose height at a point is equal to the intensity of the image at that point. A single sample is then a “spike;” the spike is located at the position of the sample and its height is equal to the intensity associated with that sample. The discrete image is a set of spikes, and the continuous image is a smooth surface fitting the spikes as shown in Figure 9.1. One obvious method of forming the continuous surface is to interpolate between the samples. 1

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2 CHAPTER9.BASICSIGNALPROCESSING Figure 9.1: A continuous image reconstructed from a discrete image represented as a set of samples. In this figure, the image is drawn as a surface whose height is equal to the intensity. Sampling We can make a digital image from an analog image by taking samples. Most simply, each sample records the value of the image intensity at a point. Consider a CCD camera. A CCD camera records image values by turning light energy into electrical energy. The light sensitive area consist of an array of small cells; each cell produces a single value, and hence, samples the image. Notice that each sample is the result of all the light falling on a single cell, and corresponds to an integral of all the light within a small solid angle (see Figure 9.2). Your eye is similar, each sample results from the action of a single photoreceptor. However, just like CCD cells, photoreceptor cells are packed together in your retina and integrate over a small area. Although it may seem like the fact that an individual cell of a CCD camera, or of your retina, samples over an area is less than ideal, the fact that intensities are averaged in this way will turn out to be an important feature of the
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Basic signals FT - Chapter 9 Basic Signal Processing...

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