Optimal Filters in the Frequency Domain

We now investigate the design of noise reduction filters in the frequency domain, which is an alternative to the time-domain approach studied in the previous chapter. In the real world, frequency-domain filters are, by far, the most popular methods. This is mainly because: 1) the filters at different frequencies (or frequency bands) are designed and handled independently with each other, therefore there is a significant flexibility in dealing with colored noise; 2) most of our knowledge and understanding of speech production and perception is related to frequencies; and 3) thanks to the fast Fourier transform (FFT), the implementation of frequency-domain filters are generally very efficient. So, in this chapter, we develop some widely used classical frequency-domain filters and discuss their properties.