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reconstruction filter
In a mixed-signal system (analog and digital), a reconstruction filter (or anti-imaging filter) is used to construct a smooth analog signal from a digital input, as in the case of a digital to analog converter (DAC) or other sampled data output device.
==Sampled data reconstruction filters==
The sampling theorem describes why the input of an ADC requires a low-pass analog electronic filter, called the anti-aliasing filter: the sampled ''input'' signal must be bandlimited to prevent aliasing (here meaning waves of higher frequency being ''recorded'' as a lower frequency).
For the same reason, the output of a DAC requires a low-pass analog filter, called a reconstruction filter - because the ''output'' signal must be bandlimited, to prevent imaging (meaning Fourier coefficients being reconstructed as spurious high-frequency 'mirrors'). This is an implementation of the Whittaker–Shannon interpolation formula.
Ideally, both filters should be brickwall filters, constant phase delay in the pass-band with constant flat frequency response, and zero response from the Nyquist frequency. This is given by a filter with a 'sinc' impulse response.
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