A transfer function is a mathematical description of how an input signal is changed into an output signal. Transfer functions can be expressed in either the time or frequency domain. Filtering is perhaps the most common type of transfer function and possibly the most common type of signal processing operation. The aim of filtering is to reject (attenuate) unwanted parts of the recorded signal and enhance (amplify) the part of the signal that contains the information of interest. The mathematical description of these changes in the signal is the transfer function of the effects of the filter. Filtering can be performed on both analog and digital signals and can be operated in both the time and frequency domains. In this chapter we will discuss how filtering is performed for the purposes of improving signal-to-noise ratio, prevention of aliasing when sampling, and reconstruction of digital signals into analog form.
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