How DSP Filters Work (Without Complex Math)
Will C. Pirkle · 2019
DSP filter theory involves complex algebra, that is, the algebra of complex numbers that involve the -1. Complex numbers contain real and imaginary parts. This chapter approaches the problem from a higher level and apply some math concepts to get the same results but without needing to keep track of a bunch of audio samples. The frequency response plot shows how a filter modifies the frequency content of a signal. In a feed-forward filter, the amount of time smearing is equal to the maximum delayed path through the feed-forward branches. Linear phase filters shift the phase of the output signal linearly across the entire frequency range. These are interesting for two reasons: first, this kind of response cannot be obtained from an analog filter. Second, this kind of filter has useful applications where phase linearity across the spectrum is important, such as filters for loudspeaker crossovers.