ABSTRACT
This chapter focuses on the discussion of the discrete Fourier transform in its application to digital filters. It discusses Nyquist's criteria for capturing or digitization of continuous signals, showing examples of simple digital filters and discussing the artifacts that arise during digital filtering. One of the main applications for the digital Fourier transform (DFT) is digital filtering, that is, reducing unwanted frequency components or boosting the desired ones. People all have seen it in the form of an equalizer in a music player, which allows one to adjust the loudness of low-frequency components (bass) relative to the middle- and the high-frequency components (treble) of the sound spectrum. It used to be done with analog electronics components filters, but these days, with the proliferation of micro controllers, it is often done digitally via the DFT. The low-pass filter is a filter that strongly suppresses or attenuates high-frequency components of the spectrum, while keeping low-frequency components mostly intact.
