However, this filter means that there is an inherent effect of the zero-order hold on the effective frequency response of the DAC resulting in a mild roll-off of gain at the higher frequencies (often a 3.9224 dB loss at the Nyquist frequency) and depending on the filter, phase distortion. These are typically removed with a low pass filter acting as a reconstruction filter. The fact that practical DACs output a sequence of piecewise constant values or rectangular pulses would cause multiple harmonics above the nyquist frequency. Piecewise constant signal typical of a zero-order (non-interpolating) DAC output. This is equivalent to a zero-order hold operation and has an effect on the frequency response of the reconstructed signal. The effect of this is that the output voltage is held in time at the current value until the next input number is latched resulting in a piecewise constant or 'staircase' shaped output. These numbers are written to the DAC, typically with a clock signal that causes each number to be latched in sequence, at which time the DAC output voltage changes rapidly from the previous value to the value represented by the currently latched number. Instead of impulses, usually the sequence of numbers update the analogue voltage at uniform sampling intervals. Increasing the digital resolution (i.e., increasing the number of bits used in each sample) or introducing sampling dither can reduce this error. However, even with an ideal reconstruction filter, digital sampling introduces quantization error that makes perfect reconstruction practically impossible. Other DAC methods (e.g., methods based on Delta-sigma modulation) produce a pulse-density modulated signal that can then be filtered in a similar way to produce a smoothly-varying signal.īy the Nyquist–Shannon sampling theorem, sampled data can be reconstructed perfectly provided that its bandwidth meets certain requirements (e.g., a baseband signal with bandwidth less than the Nyquist frequency). In particular, DACs are often used to convert finite-precision time series data to a continually-varying physical signal.Ī typical DAC converts the abstract numbers into a concrete sequence of impulses that are then processed by a reconstruction filter using some form of interpolation to fill in data between the impulses. Signal of a typical interpolating DAC output.Ī DAC converts an abstract finite-precision number (usually a fixed-point binary number) into a concrete physical quantity (e.g., a voltage or a pressure).

Analog to digital converter wikipedia