Цифрлық сигналды аналогтық сигналға түрлендіру сүзгісі

Filter used to construct a smooth analog signal from a digital input
In a mixed signal system (analog and digital), a reconstruction filter, sometimes called an 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.

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 can be achieved by a filter with a 'sinc' impulse response.

While in theory a DAC outputs a series of discrete Dirac impulses, in practice, a real DAC outputs pulses with finite bandwidth and width. Both idealized Dirac pulses, zero order held steps and other output pulses, if unfiltered, would contain spurious high frequency replicas, "or images" of the original bandlimited signal. Thus, the reconstruction filter smooths the waveform to remove image frequencies (copies) above the Nyquist limit. In doing so, it reconstructs the continuous time signal (whether originally sampled, or modelled by digital logic) corresponding to the digital time sequence. Practical filters have non flat frequency or phase response in the pass band and incomplete suppression of the signal elsewhere. The ideal sinc waveform has an infinite response to a signal, in both the positive and negative time directions, which is impossible to perform in real time – as it would require infinite delay. Consequently, real reconstruction filters typically either allow some energy above the Nyquist rate, attenuate some in band frequencies, or both. For this reason, oversampling may be used to ensure that frequencies of interest are accurately reproduced without excess energy being emitted out of band. In systems that have both, the anti aliasing filter and a reconstruction filter may be of identical design. For example, both the input and the output for audio equipment may be sampled at 44.1 kHz. In this case, both audio filters block as much as possible above 22 kHz and pass as much as possible below 20 kHz. Alternatively, a system may have no reconstruction filter and simply tolerate some energy being wasted reproducing higher frequency images of the primary signal spectrum.