reconstructionfilter

A reconstruction filter is a low-pass filter placed after a digital-to-analog converter to recover a continuous-time signal from a sequence of discrete samples. Its primary function is to suppress spectral images that arise from sampling and to smooth the stepped output into a faithful analog waveform.

In theory, ideal reconstruction uses sinc interpolation, which would perfectly reconstruct the original signal if the impulse response were infinite in duration. In the frequency domain, this corresponds to passing frequencies up to the Nyquist limit (half the sampling rate, fs/2) while completely attenuating replicas of the spectrum centered at multiples of fs. Real-world implementations approximate this behavior with a practical analog low-pass filter, which introduces some passband ripple and phase distortion.

Implementation typically involves an analog low-pass network realized with resistor-capacitor (RC), inductor-capacitor (LC), or active op-amp topologies. In oversampling and delta-sigma DACs, a digital reconstruction or interpolation filter may precede the DAC to ease the requirements on the analog stage, sometimes followed by a compensating analog stage to correct for the DAC’s own impulse response, such as that produced by a zero-order hold.

Design considerations include selecting a cutoff near fs/2 while accounting for filter roll-off, passband flatness, and phase linearity. The filter must attenuate image components without introducing excessive delay or distortion in the signal’s useful band. Its interaction with the DAC’s output stage and any prior processing (digital or analog) is also a key factor.

Applications of reconstruction filters span audio DACs, video and communications systems, and precision instrumentation where accurate conversion from digital samples to smooth analog signals is required.