TEMPORAL AND SPATIAL SIGNAL PROCESSING
6.1 CHAPTER OBJECTIVES
On completion of this chapter, the reader should be able to:
1. explain and use correlation as a signal processing tool.
2. be able to derive the correlation equations for some mathematically defined signals.
3. derive the operating equations for system identification in terms of correlation.
4. derive the equations for signal extraction when the signal is contaminated by noise, and explain the underlying assumptions behind the theory.
5. derive the equations for linear prediction and optimal filtering.
6. write down the basic equations used in tomography for reconstruction of an object’s interior from cross-sectional measurements.
Signals, by definition, are varying quantities. They may vary over time (temporal) or over an x−y plane (spatial), over three dimensions, or perhaps over time and space (e.g., a video sequence). Understanding how signals change over time (or space) helps us in several key application areas. Examples include extracting a desired signal when it is mixed with noise, identifying (or at least, estimating) the coefficients of a system, and reconstructing a signal from indirect measurements (tomography).
The term “correlation” means, in general, the similarity between two sets of data. As we will see, in signal processing, it has a more precise meaning. Correlation in signal processing has a variety of applications, including removal of random noise ...