The Scientist and Engineer's Guide to Digital Signal Processing ...
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2009-10-01
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CHAPTER
5
Linear Systems
Most DSP techniques are based on a divide-and-conquer strategy called superposition. The
signal being processed is broken into simple components, each component is processed
individually, and the results reunited. This approach has the tremendous power of breaking a
single complicated problem into many easy ones. Superposition can only be used with linear
systems, a term meaning that certain mathematical rules apply. Fortunately, most of the
applications encountered in science and engineering fall into this category. This chapter presents
the foundation of DSP: what it means for a system to be linear, various ways for breaking signals
into simpler components, and how superposition provides a variety of signal processing
techniques.
Signals and Systems
A signal is a description of how one parameter varies with another parameter.
For instance, voltage changing over time in an electronic circuit, or brightness
varying with distance in an image. A system is any process that produces an
output signal in response to an input signal. This is illustrated by the block
diagram in Fig. 5-1. Continuous systems input and output continuous signals,
such as in analog electronics. Discrete systems input and output discrete
signals, such as computer programs that manipulate the values stored in arrays.
Several rules are used for naming signals. These aren't always followed in
DSP, but they are very common and you should memorize them. The
mathematics is difficult enough without a clear notation. First, continuous
signals use parentheses, such as: and , while discrete signals usex(t) y(t)
brackets, as in: and . Second, signals use lower case letters. Upperx[n] y[n]
case letters are reserved for the frequency domain, discussed in later chapters.
Third, the name given to a signal is usually descriptive of the parameters it
represents. For example, a voltage depending on time might be called: , orv(t)
a stock market price measured each day could be: .p[d]
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