An Observation about the Modern Application of Sinc Filters

One of the facts which I have blogged about before, was that an important type of filter, which was essentially digital, except for its first implementations, was called a ‘Sinc Filter‘. This filter was once presented as an ideal low-pass filter, that was also a brick-wall filter, meaning, that as the series was made longer, near-perfect cutoff was achieved.

Well, while the use of this filter in its original form has largely been deprecated, there is a modern version of it that has captured some popularity. The Sinc Filter is nowadays often combined with a ‘Kaiser Window‘, and doing so accomplishes two goals:

  • The Kaiser Window puts an end to the series being an infinite series, which many coders had issues with,
  • It also makes possible Sinc Filters with cutoff-frequencies, that are not negative powers of two, times the Nyquist Frequency.

It has always been possible to design a Sinc Filter with 2x or 4x over-sampling, and in some frivolous examples, with 8x over-sampling. But if a Circuit Designer ever tried to design one, that has 4.3 over-sampling, for example, thereby resulting in a cutoff-frequency which is just lower than 1/4 the Nyquist Frequency, the sticky issue would always remain, as to what would take place with the last zero-crossing of the Sinc Function, furthest from the origin. It could create a mess in the resulting signal as well.

Because the Kaiser Windowing Function actually goes to zero gradually, it suppresses the farthest zero-crossings of the Sinc Function from the origin, without impeding that the filter still works essentially, as the Math of the Sinc Function would suggest.

Further, even Linux utilities such as ‘ffmpeg’, employ a Sinc Filter by default when resampling an audio stream, but with a Kaiser Window.

(Updated 8/06/2019, 15h35 … )

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