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 f0 is to be determined when the signal is sampled at frequency fs > 2f0. 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 ƒ0. 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 ƒ0 which is to be detected is present, threshold logic provides the logic information.
This process can be analyzed as follows. Assume s0(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 ip(t) in phase with s0, and of unit amplitude. Using equation (1.6), we can write:
in which:
The signal obtained after rectification is:
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