# 17Applications

Signal processing is instrumental in the generalization of electronics to all technical fields. A few examples of applications are presented in this chapter, mainly in the field of communications.

## 17.1 Frequency Detection

Assume that the amplitude of a signal component with frequency *f*_{0} is to be determined when the signal is sampled at frequency *f*_{s} > 2*f*_{0}. Figure 17.1 represents the set of operations to be performed.

The signal is applied to a narrow band-pass filter centered on the frequency ƒ_{0}. Rectification is then performed by taking the absolute value of the numbers obtained. This set of absolute values is applied to a low-pass filter which provides the desired value of the amplitude. If the frequency component ƒ_{0} which is to be detected is present, threshold logic provides the logic information.

This process can be analyzed as follows. Assume *s*_{0}(*t*) is the signal to be detected, with:

Taking the absolute value of the numbers which represent samples of this signal is equivalent to multiplying by a square wave *i*_{p}(*t*) in phase with *s*_{0}, and of unit amplitude. Using equation (1.6), we can write:

in which:

The signal obtained after rectification is:

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