Analog signals are usually signals defined over continuous independent variable(s). Modeling the Speech Signal is produced by your vocal cords exciting acoustic resonances in your vocal tract. The result is pressure waves propagating in the air, and the speech signal thus corresponds to a function having independent variables of space and time and a value corresponding to air pressure: s (x, t) (Here we use vector notation x to denote spatial coordinates). When you record someone talking, you are evaluating the speech signal at a particular spatial location, x0 say. An example of the resulting waveform s (x0,t) is shown in this Figure 1.1.
Speech Example
Photographs are static, and are continuous-valued signals defined over space. Black-and-white images have only one value at each point in space, which amounts to its optical refection properties. In Figure 1.2, an image is shown, demonstrating that it (and all other images as well) are functions of two independent spatial variables.
Color images have values that express how reflectivity depends on the optical spectrum. Painters long ago found that mixing together combinations of the so-called primary colors red, yellow and blue can produce very realistic color images. Thus, images today are usually thought of as having three values at every point in space, but a different set of colors is used: How much of red, green and blue is present. Mathematically, color pictures are multivalued vector-valued signals: s (x)=(r (x) ,g (x) ,b (x))T .
Interesting cases abound where the analog signal depends not on a continuous variable, such as time, but on a discrete variable. For example, temperature readings taken every hour have continuous analog values, but the signal's independent variable is (essentially) the integers.
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