Sinc filter Totally Explained

Everything about Sinc Filter totally explained

In signal processing, a sinc filter is an idealized filter that removes all frequency components above a given bandwidth, leaves the low frequencies alone, and has linear phase. The filter's impulse response is a sinc function in the time domain, and its frequency response is a rectangular function.
Realistic filters can only approximate this ideal, since an ideal sinc filter (aka rectangular filter) has an infinite delay, but it's commonly found in conceptual demonstrations or proofs, such as the sampling theorem and the Whittaker–Shannon interpolation formula.
In mathematical terms, the desired frequency response is the rectangular function:
ť

H(f) = mathrm

Interestingly enough, the name sinc filter is applied also to the filter shape that's rectangular in time and sinx/x (sinc) in frequency. How to tell which version is being used? The traditional DSP literature, like http://www.dspguide.com/ uses the description above. As the sinc-in-time filter has infinite impulse response and must be approximated for real-world applications, it's often a "windowed sinc filter." Sinc-in-frequency filters, among many other applications, are almost universally used for decimating Sigma-Delta ADCs, as they're easy to implement and nearly optimum for this use. Papers on Sigma-Delta ADCs (such as Time domain analysis of sigma delta modulation, Chou, W.; Meng, T.H.; Gray, R.M. Acoustics, Speech, and Signal Processing, 1990. ICASSP-90., 1990 International Conference Acoustic Signal Processing, 3-6 April 1990 P. 1751 - 1754 vol.3, or www.us.design-reuse.com/articles/10028/understanding-cascaded-integrator-comb-filters.html) will use the second version.

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Everything about Sinc Filter totally explained

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