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In signal processing, a sinc filter is an idealized filter that removes all frequency components above a given bandwidth and leaves the low frequencies alone. It is shaped like a rectangular function in the frequency domain and like a sinc function in the time domain. Realistic filters can only approximate this, since an ideal sinc filter (aka rectangular filter) has an infinite delay, but it is commonly found in conceptual demonstrations or proofs, such as the sampling theorem and the Whittaker–Shannon interpolation formula. Signal processing is the processing, amplification and interpretation of signals, and deals with the analysis and manipulation of signals. ...
Television signal splitter consisting of a hi-pass and a low-pass filter. ...
The rectangular function (also known as the rectangle function or the normalized boxcar function) is defined as or in terms of the Heaviside step function The rectangular function is normalized: The Fourier transform of the rectangular function is where sinc is the sinc function. ...
The sinc function sinc(x) from x = −8π to 8π. In mathematics, the sinc function (for sinus cardinalis), also known as the interpolation function, filtering function or the first spherical Bessel function , is the product of a sine function and a monotonically decreasing function. ...
The Nyquist–Shannon sampling theorem is a fundamental result in the field of information theory, in particular telecommunications and signal processing. ...
The Whittaker–Shannon interpolation formula dates back to works of E. Borel in 1898, and E. T. Whittaker in 1915, and was cited from works of J. M. Whittaker in 1935 in the formulation of the Nyquist–Shannon sampling theorem by C. E. Shannon in 1949. ...
In mathematical terms, the desired frequency response is the rectangular function : The rectangular function (also known as the rectangle function or the normalized boxcar function) is defined as or in terms of the Heaviside step function The rectangular function is normalized: The Fourier transform of the rectangular function is where sinc is the sinc function. ...
 where  is an arbitrary cutoff frequency (aka bandwidth) (in Hz). The impulse response of such a filter is given by the inverse Fourier transform: In mathematics, the continuous Fourier transform is a certain linear operator that maps functions to other functions. ...
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The sinc function sinc(x) from x = −8π to 8π. In mathematics, the sinc function (for sinus cardinalis), also known as the interpolation function, filtering function or the first spherical Bessel function , is the product of a sine function and a monotonically decreasing function. ...
See also - Aliasing
- Anti-aliasing
- Whittaker–Shannon interpolation formula
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, in terms of the normalized 
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